[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/5560#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/5560","headline":"Grittions Guived -Wikipedia\u3001The Free Encyclopedia","name":"Grittions Guived -Wikipedia\u3001The Free Encyclopedia","description":"before-content-x4 \u66f2\u7dda\u4e0b\u306e\u9818\u57df\u3092\u8fd1\u4f3c\u3059\u308b\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u65b9\u6cd5\u306e4\u3064 \u6570\u5b66\u3067\u306f\u3001 Suma de Riemann \u3053\u308c\u306f\u3001\u6709\u9650\u5408\u8a08\u306b\u3088\u308b\u7a4d\u5206\u306e\u5024\u306e\u8fd1\u4f3c\u306e\u4e00\u7a2e\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u4e16\u7d00\u306e\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u8005\u306b\u656c\u610f\u3092\u8868\u3057\u3066\u305d\u3046\u3067\u3059 xix \u3001\u30d9\u30eb\u30f3\u30cf\u30eb\u30c8\u30fb\u30ea\u30fc\u30de\u30f3\u3002 after-content-x4 \u5408\u8a08\u306f\u3001\u9818\u57df\u3092\u30d5\u30a9\u30fc\u30e0\uff08\u9577\u65b9\u5f62\u3001\u53f0\u5f62\u3001\u6b63\u65b9\u5f62\u3001\u4e09\u89d2\u5f62\u3001\u305f\u3068\u3048\u8a71\u3001\u307e\u305f\u306f\u7acb\u65b9\u4f53\uff09\u306b\u5206\u5272\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u306b\u4f3c\u305f\u9818\u57df\u3092\u5f62\u6210\u3057\u3001\u3053\u308c\u3089\u306e\u5404\u5f62\u5f0f\u306e\u9818\u57df\u3092\u8a08\u7b97\u3057\u3001\u6700\u5f8c\u306b\u3053\u308c\u3089\u3059\u3079\u3066\u306e\u5c0f\u3055\u306a\u9818\u57df\u3092\u4e00\u7dd2\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u7528\u3057\u3066\u3001\u8a08\u7b97\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7406\u304c\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3092\u9589\u3058\u305f\u3082\u306e\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u5bb9\u6613\u306b\u3057\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u5b9a\u7fa9\u3055\u308c\u305f\u7a4d\u5206\u306e\u6570\u5024\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 5 \u5c0f\u3055\u306a\u5f62\u3067\u6e80\u305f\u3055\u308c\u305f\u9818\u57df\u306f\u3001\u4e00\u822c\u306b\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u3068\u307e\u3063\u305f\u304f\u540c\u3058\u5f62\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u306f\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u30a8\u30e9\u30fc\u306f\u3001\u9818\u57df\u3092\u3088\u308a\u7d30\u304b\u304f\u7d30\u304b\u304f\u4f7f\u7528\u3057\u3066\u3001\u9818\u57df\u3092\u3088\u308a\u7d30\u304b\u304f\u5206\u5272\u3059\u308b\u3053\u3068\u3067\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d5\u30a9\u30fc\u30e0\u304c\u5c0f\u3055\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3001\u5408\u8a08\u306f\u7a4d\u5206\u30c7\u30ea\u30fc\u30de\u30f3\u306b\u8fd1\u3065\u3044\u3066\u3044\u307e\u3059\u3002 Table of Contents after-content-x4 \u610f\u5473 [ \u7de8\u96c6\u3057\u307e\u3059","datePublished":"2023-12-19","dateModified":"2023-12-19","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/2\/2a\/Riemann_sum_convergence.png\/300px-Riemann_sum_convergence.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/2\/2a\/Riemann_sum_convergence.png\/300px-Riemann_sum_convergence.png","height":"300","width":"300"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/5560","wordCount":11155,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u66f2\u7dda\u4e0b\u306e\u9818\u57df\u3092\u8fd1\u4f3c\u3059\u308b\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u65b9\u6cd5\u306e4\u3064 \u6570\u5b66\u3067\u306f\u3001 Suma de Riemann \u3053\u308c\u306f\u3001\u6709\u9650\u5408\u8a08\u306b\u3088\u308b\u7a4d\u5206\u306e\u5024\u306e\u8fd1\u4f3c\u306e\u4e00\u7a2e\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u4e16\u7d00\u306e\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u8005\u306b\u656c\u610f\u3092\u8868\u3057\u3066\u305d\u3046\u3067\u3059 xix \u3001\u30d9\u30eb\u30f3\u30cf\u30eb\u30c8\u30fb\u30ea\u30fc\u30de\u30f3\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5408\u8a08\u306f\u3001\u9818\u57df\u3092\u30d5\u30a9\u30fc\u30e0\uff08\u9577\u65b9\u5f62\u3001\u53f0\u5f62\u3001\u6b63\u65b9\u5f62\u3001\u4e09\u89d2\u5f62\u3001\u305f\u3068\u3048\u8a71\u3001\u307e\u305f\u306f\u7acb\u65b9\u4f53\uff09\u306b\u5206\u5272\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u306b\u4f3c\u305f\u9818\u57df\u3092\u5f62\u6210\u3057\u3001\u3053\u308c\u3089\u306e\u5404\u5f62\u5f0f\u306e\u9818\u57df\u3092\u8a08\u7b97\u3057\u3001\u6700\u5f8c\u306b\u3053\u308c\u3089\u3059\u3079\u3066\u306e\u5c0f\u3055\u306a\u9818\u57df\u3092\u4e00\u7dd2\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u7528\u3057\u3066\u3001\u8a08\u7b97\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7406\u304c\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3092\u9589\u3058\u305f\u3082\u306e\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u5bb9\u6613\u306b\u3057\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u5b9a\u7fa9\u3055\u308c\u305f\u7a4d\u5206\u306e\u6570\u5024\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u30025\u5c0f\u3055\u306a\u5f62\u3067\u6e80\u305f\u3055\u308c\u305f\u9818\u57df\u306f\u3001\u4e00\u822c\u306b\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u3068\u307e\u3063\u305f\u304f\u540c\u3058\u5f62\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u306f\u6e2c\u5b9a\u3055\u308c\u3066\u3044\u308b\u9818\u57df\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u30a8\u30e9\u30fc\u306f\u3001\u9818\u57df\u3092\u3088\u308a\u7d30\u304b\u304f\u7d30\u304b\u304f\u4f7f\u7528\u3057\u3066\u3001\u9818\u57df\u3092\u3088\u308a\u7d30\u304b\u304f\u5206\u5272\u3059\u308b\u3053\u3068\u3067\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d5\u30a9\u30fc\u30e0\u304c\u5c0f\u3055\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3001\u5408\u8a08\u306f\u7a4d\u5206\u30c7\u30ea\u30fc\u30de\u30f3\u306b\u8fd1\u3065\u3044\u3066\u3044\u307e\u3059\u3002 Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u610f\u5473 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u3044\u304f\u3064\u304b\u306e\u7279\u5b9a\u306e\u30bf\u30a4\u30d7\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5de6\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u53f3\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u30df\u30c3\u30c9\u30dd\u30a4\u30f3\u30c8\u30eb\u30fc\u30eb [ \u7de8\u96c6\u3057\u307e\u3059 ] SUMA Trapezoidal [ \u7de8\u96c6\u3057\u307e\u3059 ] \u7a4d\u5206\u8a08\u7b97\u3068\u306e\u95a2\u4fc2 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u53c2\u7167 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u610f\u5473 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u4ee5\u4e0b\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u6d77 f \uff1a [ a \u3001 b ] \u2192 r {displaystyle f\uff1a[a\u3001b] rightarrow mathbb {r}} \u30b3\u30f3\u30d1\u30af\u30c8\u9593\u9694\u306b\u56f2\u307e\u308c\u305f\u95a2\u6570 [ a \u3001 b ] {displaystyle [a\u3001b]} \u3002\u5404\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u3057\u3066        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4p = \u30d0\u30c4 0 \u3001 \u30d0\u30c4 \u521d\u3081 \u3001 \u30d0\u30c4 2 \u3001 \u3002 \u3002 \u3002 \u3001 \u30d0\u30c4 n {displaystyle p = x_ {0}\u3001x_ {1}\u3001x_ {2}\u3001…\u3001x_ {n}} \u306e [ a \u3001 b ] {displaystyle [a\u3001b]} \u96fb\u8a71\u3057\u307e\u3059 \u4e2d\u9593\u70b9\u306e\u5bb6\u65cf \uff08\u3068\u95a2\u9023\u3057\u305f p {displaystyle p} \uff09\u30bb\u30c3\u30c8\u306e\u3044\u305a\u308c\u304b\u306b t = { t \u521d\u3081 \u3001 t 2 \u3001 \u3002 \u3002 \u3002 \u3001 t n } {displaystyle t = {t_ {1}\u3001t_ {2}\u3001…\u3001t_ {n}}}}} \u30dd\u30a4\u30f3\u30c8\u3067\u5f62\u6210\u3055\u308c\u307e\u3059 t \u79c1 {displaystylet_ {i}} \u2208 {displaystyle in} [ \u30d0\u30c4 \u79c1  –  \u521d\u3081 \u3001 \u30d0\u30c4 \u79c1 ] {displaystyle [x_ {i-1}\u3001x_ {i}]} \u3001 \u305f\u3081\u306b \u79c1 = \u521d\u3081 \u3001 2 \u3001 \u3002 \u3002 \u3002 \u3001 n {displaystyle i = 1,2\u3001…\u3001n} \u3002 \u547c\u3070\u308c\u3066\u3044\u307e\u3059 Suma de Riemann \u306e f {displaystyle f} \u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u95a2\u9023\u3057\u307e\u3059 p {displaystyle p} \u305d\u3057\u3066\u3001\u5bfe\u5fdc\u3059\u308b\u30dd\u30a4\u30f3\u30c8\u306e\u5bb6\u65cf\u306b t {displaystylet} \u3001\u756a\u53f7\u306b a \uff08 p \u3001 t \uff09\uff09 = \u2211 \u79c1 = \u521d\u3081 n f \uff08 t \u79c1 \uff09\uff09 d \u30d0\u30c4 \u79c1 {displaystyle sigma\uff08p\u3001t\uff09= sum _ {i = 1}^{n} f\uff08t_ {i}\uff09delta x_ {i}} \u3069\u3053 d \u30d0\u30c4 \u79c1 = \u30d0\u30c4 \u79c1  –  \u30d0\u30c4 \u79c1  –  \u521d\u3081 {displaystyle delta x_ {i} = x_ {i} -x_ {i-1}} \u3002 \u6d77 p {displaystyle p} \u3044\u305a\u308c\u304b\u306e\u56fa\u5b9a\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3 [ a \u3001 b ] {displaystyle [a\u3001b]} \u3002\u3068 t {displaystylet} \u305d\u308c\u306f\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u5fdc\u3059\u308b\u4efb\u610f\u306e\u4e2d\u9593\u70b9\u306e\u5bb6\u65cf\u3067\u3059 p {displaystyle p} \u3001 \u305d\u308c\u3067 \u4f4e\u984d  l \uff08 p \uff09\uff09 {displaystyle l\uff08p\uff09} \u3068 \u4e0a\u9577  \u306e \uff08 p \uff09\uff09 {displaystyleu\uff08p\uff09} \u3068\u30ea\u30fc\u30de\u30f3 a \uff08 p \u3001 t \uff09\uff09 {displaystyle sigma\uff08p\u3001t\uff09} \u5f7c\u3089\u306f\u305d\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff1a L(P){displaystyle l\uff08p\uff09} \u2264  \u03c3(P,T){displaystyle sigma\uff08p\u3001t\uff09} \u2264  U(P){displaystyleu\uff08p\uff09} \u3001 \u2200T\u2208A{displaystyle forall tin mathbb {a}} L(P)=inf{\u03c3(P,T):T\u2208A}{displaystyle l\uff08p\uff09= inf {sigma\uff08p\u3001t\uff09\uff1atin mathbb {a}}}} U(P)=sup\u00a0{\u03c3(P,T):T\u2208A}{displaystyle u\uff08p\uff09= sup {sigma\uff08p\u3001t\uff09\uff1atin mathbb {a}}}}} \u3069\u3053 A{displaystyle mathrm {mathbb {a}}} \u3053\u308c\u306f\u3001\u6307\u5b9a\u3055\u308c\u305f\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306b\u5bfe\u5fdc\u3059\u308b\u4e2d\u9593\u70b9\u30d5\u30a1\u30df\u30ea\u306e\u30bb\u30c3\u30c8\u3067\u3059\uff08\u56fa\u5b9a\uff09 P{displaystyle p} \u3002 [ \u521d\u3081 ] \u200b \u3044\u304f\u3064\u304b\u306e\u7279\u5b9a\u306e\u30bf\u30a4\u30d7\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u3068 ti{displaystylet_ {i}} = xi\u22121{displaystyle x_ {i-1}} \u3059\u3079\u3066\u306e\u305f\u3081\u306b \u79c1 \u3001\u6b21\u306b\u96fb\u8a71\u3057\u307e\u3059 s \u3068\u3057\u3066 \u5de6\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 \u3002 \u3068 ti{displaystylet_ {i}} = xi{displaystyle x_ {i}} \u3001\u6b21\u306b\u96fb\u8a71\u3057\u307e\u3059 s \u3068\u3057\u3066 \u53f3\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 \u3002 \u3068 ti=(xi+xi\u22121)\/2{displaystyle t_ {i} =\uff08x_ {i}+x_ {i-1}\uff09\/2} \u79c1\u304c\u3059\u3079\u3066\u306b\u547c\u3070\u308c\u307e\u3059 \u30df\u30c3\u30c9\u30dd\u30a4\u30f3\u30c8\u30eb\u30fc\u30eb o to Riemann\u30e1\u30c7\u30a3\u30a2\u306e\u5408\u8a08 \u3002 \u3068 f(ti)=supf([xi\u22121,xi]){displaystyle f\uff08t_ {i}\uff09= sup f\uff08[x_ {i-1}\u3001x_ {i}]}} \uff08\u3064\u307e\u308a\u3001\u6700\u9ad8\u306ef [xi\u22121,xi]{displaystyle [x_ {i-1}\u3001x_ {i}]} \u3001\u6b21\u306b\u3001s\u306fa\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059 \u30b9\u30fc\u30da\u30ea\u30a2\u30ea\u30fc\u30de\u30f3\u30fb\u30b9\u30de \u307e\u305f\u306f1\u3064 \u3088\u308a\u9ad8\u3044\u30c0\u30eb\u30d6\u30fc \u3002 \u3068 f(ti)=inff([xi\u22121,xi]){displaystyle f\uff08t_ {i}\uff09= inf f\uff08[x_ {i-1}\u3001x_ {i}]}} \uff08\u3064\u307e\u308a\u3001F\u306e4\u756a\u76ee\u306f\u7d42\u308f\u308a\u307e\u3059 [xi\u22121,xi]{displaystyle [x_ {i-1}\u3001x_ {i}]} \u3001\u6b21\u306b\u3001s\u306fa\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059 \u30ed\u30fc\u30fb\u30ea\u30fc\u30de\u30f3\u30fb\u30b9\u30de\u30fb\u30c7\u30fb\u30ea\u30fc\u30de\u30f3 \u307e\u305f\u306f1\u3064 \u4e0b\u306e\u30c0\u30eb\u30d6\u30fc \u3002 \u3053\u308c\u3089\u3059\u3079\u3066\u306e\u65b9\u6cd5\u306f\u3001\u6570\u5024\u7d71\u5408\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306e\u6700\u3082\u57fa\u672c\u7684\u306a\u5f62\u5f0f\u306e1\u3064\u3067\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u3059\u3079\u3066\u306eRiemann\u306e\u5408\u8a08\u304c\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u3068\u3057\u3066\u53ce\u675f\u3059\u308b\u5834\u5408\u3001\u95a2\u6570\u306fRiemann\u306b\u3088\u3063\u3066\u7d71\u5408\u3055\u308c\u307e\u3059\u00ab \u307e\u3059\u307e\u3059\u3046\u307e\u304f\u3044\u304d\u307e\u3059 \u00bb\u3002 \u6280\u8853\u7684\u306b\u306fRiemann\u306e\u5408\u8a08\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001Riemann\u306e\u5de6\u53f3\u306e\u5408\u8a08\u306e\u5e73\u5747\u306f\u53f0\u5f62\u306e\u5408\u8a08\u3067\u3042\u308a\u3001\u52a0\u91cd\u5e73\u5747\u3092\u4f7f\u7528\u3057\u3066\u5305\u62ec\u7684\u306a\u5305\u62ec\u7684\u306a\u6982\u5ff5\u3092\u8fd1\u4f3c\u3059\u308b\u6700\u3082\u5358\u7d14\u3067\u6700\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u306e1\u3064\u3067\u3059\u3002\u3053\u308c\u306b\u7d9a\u3044\u3066\u3001\u30b7\u30f3\u30d7\u30bd\u30f3\u30eb\u30fc\u30eb\u3068\u30cb\u30e5\u30fc\u30c8\u30f3\u30b3\u30fc\u30c8\u5f0f\u304c\u7d9a\u304d\u307e\u3059\u3002 \u7279\u5b9a\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u5185\u306eRiemann\u306e\u5408\u8a08\uff08\u3064\u307e\u308a\u3001\u3069\u3093\u306a\u9078\u629e\u3067\u3082 t i{displaystylet_ {i}} \u305d\u306e\u9593\u306b \u30d0\u30c4 i\u22121{displaystyle x_ {i-1}} \u3068 \u30d0\u30c4 i{displaystyle x_ {i}} \uff09\u3002\u305d\u308c\u306f\u3001\u4e0b\u90e8\u3068\u4e0a\u90e8\u306e\u30c0\u30eb\u30d6\u30fc\u548c\u306e\u9593\u306b\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6700\u7d42\u7684\u306bRiemann\u306e\u7a4d\u5206\u306b\u76f8\u5f53\u3059\u308bDarboux\u7a4d\u5206\u306e\u57fa\u790e\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 \u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u306e4\u3064\u306e\u65b9\u6cd5\u306f\u3001\u901a\u5e38\u3001\u540c\u3058\u30b5\u30a4\u30ba\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u3067\u30a2\u30d7\u30ed\u30fc\u30c1\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9593\u9694 [ a \u3001 b ] {displaystyle [a\u3001b]} \u3067\u5206\u304b\u308c\u3066\u3044\u307e\u3059 n Subintervalos\u3001\u305d\u308c\u305e\u308c\u9577\u3055 d \u30d0\u30c4 = b\u2212an {displaystyle delta x = {frac {b-a} {n}}} \u3002\u305d\u306e\u5f8c\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 a \u3001 a + d \u30d0\u30c4 \u3001 a + 2 d \u30d0\u30c4 \u3001 … \u3001 a + \uff08 n  –  2 \uff09\uff09 d \u30d0\u30c4 \u3001 a + \uff08 n  –  \u521d\u3081 \uff09\uff09 d \u30d0\u30c4 \u3001 b {displayStyle A\u3001A+Delta X\u3001A+2\u3001Delta X\u3001LDOTS\u3001A+\uff08N-2\uff09\u3001Delta X\u3001A+\uff08N-1\uff09\u3001Delta X\u3001B} \u3002  Riemann\u3092\u5de6\u306b\u5408\u8a08\u3057\u307e\u3059 x3{displaystyle x^{3}} 4\u3064\u306e\u4e0b\u4f4d\u533a\u5206\u3092\u4f7f\u7528\u3059\u308b[0.2]\u306b\u3064\u3044\u3066 \u5de6\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5de6\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08\u306e\u305f\u3081\u306b\u3001\u5de6\u7aef\u306e\u30dd\u30a4\u30f3\u30c8\u3067\u306e\u305d\u306e\u5024\u306b\u5bfe\u3059\u308b\u95a2\u6570\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u30d9\u30fc\u30b9\u3068\u8907\u6570\u306e\u9577\u65b9\u5f62\u3092\u63d0\u4f9b\u3057\u307e\u3059 d \u30d0\u30c4 {displaystyle delta x} \u3068\u9ad8\u3055 f \uff08 a + \u79c1 d \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08a+idelta x\uff09} \u3002\u3053\u308c\u3092\u884c\u3046 \u79c1 = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 \u3002 \u3002 \u3002 \u3001 n  –  \u521d\u3081 {displaystyle i = 0,1,2\u3001…\u3001n-1} \u30a8\u30ea\u30a2\u3092\u8ffd\u52a0\u3057\u307e\u3059 d \u30d0\u30c4 [ f \uff08 a \uff09\uff09 + f \uff08 a + d \u30d0\u30c4 \uff09\uff09 + f \uff08 a + 2 d \u30d0\u30c4 \uff09\uff09 + \u22ef + f \uff08 b  –  d \u30d0\u30c4 \uff09\uff09 ] {displaystyle delta xleft [f\uff08a\uff09+f\uff08a+delta x\uff09+f\uff08a+2\u3001delta x\uff09+cdots+f\uff08b-delta x\uff09\u53f3]} \u3002 \u30ea\u30fc\u30de\u30f3\u306e\u5de6\u306e\u5408\u8a08\u306f\u3001\u904e\u5927\u8a55\u4fa1\u306b\u7b49\u3057\u3044\u5834\u5408 f {displaystyle f} \u3053\u306e\u9593\u9694\u3067\u306f\u5358\u8abf\u306b\u6e1b\u5c11\u3057\u3001\u5358\u8abf\u306b\u5897\u52a0\u3059\u308b\u3068\u904e\u5c0f\u8a55\u4fa1\u3055\u308c\u307e\u3059\u3002 \u53f3\u5074\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5408\u8a08 [ \u7de8\u96c6\u3057\u307e\u3059 ]  \u30ea\u30fc\u30de\u30f3\u306e\u6b63\u3057\u3044\u5408\u8a08 x3{displaystyle x^{3}} 4\u3064\u306e\u4e0b\u4f4d\u533a\u5206\u3092\u4f7f\u7528\u3059\u308b[0.2]\u306b\u3064\u3044\u3066 f {displaystyle f} \u3053\u3053\u3067\u306f\u3001\u53f3\u7aef\u306e\u5024\u306e\u5024\u306b\u3064\u3044\u3066\u30a2\u30d7\u30ed\u30fc\u30c1\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u8907\u6570\u306e\u9577\u65b9\u5f62\u304c\u30d9\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059 d \u30d0\u30c4 {displaystyle delta x} \u3068\u9ad8\u3055 f \uff08 a + \u79c1 d \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08a+idelta x\uff09} \u3002\u3053\u308c\u3092\u884c\u3046 \u79c1 = \u521d\u3081 \u3001 2 \u3001 \u3002 \u3002 \u3002 \u3001 n {displaystyle i = 1,2\u3001…\u3001n} \u7d50\u679c\u306e\u9818\u57df\u3092\u8ffd\u52a0\u3057\u307e\u3059 d \u30d0\u30c4 [ f \uff08 a + d \u30d0\u30c4 \uff09\uff09 + f \uff08 a + 2 d \u30d0\u30c4 \uff09\uff09 + \u22ef + f \uff08 b \uff09\uff09 ] {displaystyle delta xleft [f\uff08a+delta x\uff09+f\uff08a+2\u3001delta x\uff09+cdots+f\uff08b\uff09\u53f3]} \u3002 \u30ea\u30fc\u30de\u30f3\u306e\u6b63\u3057\u3044\u5408\u8a08\u306f\u3001\u904e\u5c0f\u8a55\u4fa1\u306e\u5834\u5408\u306b\u76f8\u5f53\u3057\u307e\u3059 f {displaystyle f} \u5358\u8abf\u306b\u6e1b\u5c11\u3057\u3001\u5358\u8abf\u306b\u5897\u52a0\u3059\u308b\u3068\u904e\u5927\u8a55\u4fa1\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u5f0f\u306e\u30a8\u30e9\u30fc\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 | \u222babf \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4  –  Aright| \u2264 M1(b\u2212a)22n{displaystyle leftervert int _ {a}^{b} f\uff08x\uff09\u3001dx-a_ {mathrm {right}} rightvert leq {frac {m_ {1}\uff08b-a\uff09^{2}} {2n}}}}}  \u3069\u3053 m \u521d\u3081 {displaystyle m_ {1}} \u305d\u308c\u306f\u306e\u7d76\u5bfe\u5024\u306e\u6700\u5927\u5024\u3067\u3059 f ‘ \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f ‘\uff08x\uff09} \u3002 \u30df\u30c3\u30c9\u30dd\u30a4\u30f3\u30c8\u30eb\u30fc\u30eb [ \u7de8\u96c6\u3057\u307e\u3059 ]  \u30ea\u30fc\u30de\u30f3\u306e\u4e2d\u9593\u70b9\u306e\u5408\u8a08 x3{displaystyle x^{3}} 4\u3064\u306e\u4e0b\u4f4d\u533a\u5206\u3092\u4f7f\u7528\u3059\u308b[0.2]\u306b\u3064\u3044\u3066 \u306e\u30a2\u30d7\u30ed\u30fc\u30c1 f {displaystyle f} \u9593\u9694DA\u306e\u4e2d\u9593\u70b9\u3067 f \uff08 a + d \u30d0\u30c4 \/ 2 \uff09\uff09 {displaystyle f\uff08a+delta x\/2\uff09} \u6700\u521d\u306e\u9593\u9694\u3067\u306f\u3001\u6b21\u306e\u9593 f \uff08 a + 3 d \u30d0\u30c4 \/ 2 \uff09\uff09 {displaystyle f\uff08a+3delta x\/2\uff09} \u3001\u305d\u306e\u3088\u3046\u306a\u307e\u3067 f \uff08 b  –  d \u30d0\u30c4 \/ 2 \uff09\uff09 {displaystyle f\uff08b-delta x\/2\uff09} \u3002\u9818\u57df\u306e\u8981\u7d04\u3001\u7d50\u679c\uff1a d \u30d0\u30c4 [ f \uff08 a + \u0394x2\uff09\uff09 + f \uff08 a + 3\u0394x2\uff09\uff09 + \u22ef + f \uff08 b  –  \u0394x2\uff09\uff09 ] {displaystyle delta xleft [f\uff08a+{tfrac {delta x} {2}}\uff09+f\uff08a+{tfrac {3\u3001delta x} {2}}\uff09+cdots+f\uff08b- {tfrac {delta x}} {2}\uff09\u53f3]}} \u3002 \u3053\u306e\u5f0f\u306e\u30a8\u30e9\u30fc\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 | \u222babf \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4  –  Amid| \u2264 M2(b\u2212a)324n2{displaystyle leftervert int _ {a}^{b} f\uff08x\uff09\u3001dx-a_ {mathrm {mid}} rightvert leq {frac {m_ {2}\uff08b-a\uff09^{3}} {24n^{2}}}}}}}}  \u3069\u3053 m 2 {displaystyle m_ {2}} \u7d76\u5bfe\u5024\u306e\u6700\u5927\u5024\u3067\u3059 f ‘ ‘ \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f^{prime prime}\uff08x\uff09} \u9593\u9694\u3067\u3002 SUMA Trapezoidal [ \u7de8\u96c6\u3057\u307e\u3059 ]  Summa Riemann Riemann Riemann\u3002 x3{displaystyle x^{3}} 4\u3064\u306e\u4e0b\u4f4d\u533a\u5206\u3092\u4f7f\u7528\u3059\u308b[0.2]\u306b\u3064\u3044\u3066 \u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u306e\u5024 f \u9593\u9694\u3067\u306f\u3001\u5de6\u53f3\u306e\u7aef\u306e\u5024\u306e\u5e73\u5747\u306b\u3088\u3063\u3066\u8fd1\u4f3c\u3055\u308c\u307e\u3059\u3002\u3059\u3067\u306b\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u65b9\u6cd5\u3067\u306f\u3001\u30a8\u30ea\u30a2\u5f0f\u3092\u4f7f\u7528\u3057\u305f\u7c21\u5358\u306a\u8a08\u7b97 a = 12h \uff08 b 1+ b 2\uff09\uff09 {displaystyle a = {tfrac {1} {2}} h\uff08b_ {1}+b_ {2}\uff09} \u5e73\u884c\u306a\u5074\u9762\u3092\u6301\u3064\u7a7a\u306a\u5834\u5408 b \u521d\u3081 \u3001 b 2 \u3068\u9ad8\u3055 h \u751f\u7523 12Q [ f(a)+2f(a+Q)+2f(a+2Q)+2f(a+3Q)+\u22ef+f(b)] {displaystyle {tfrac {1} {2}} qleft [f\uff08a\uff09+2f\uff08a+q\uff09+2f\uff08a+2q\uff09+2f\uff08a+3q\uff09+cdots+f\uff08b\uff09}} \u3002 \u3053\u306e\u5f0f\u306e\u30a8\u30e9\u30fc\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 | \u222babf(x)dx\u2212Atrap| \u2264 M2(b\u2212a)312n2\u3001 {displaystyle leftervert int _ {a}^{b} f\uff08x\uff09\u3001dx-a_ {mathrm {trap}} rightvert leq {frac {m_ {2}\uff08b-a\uff09^{3}} {12n^{2}}}\u3001}}} \u3069\u3053 m 2 {displaystyle m_ {2}} \u305d\u308c\u306f\u306e\u7d76\u5bfe\u5024\u306e\u6700\u5927\u5024\u3067\u3059 f ‘ ‘ \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f^{prime prime}\uff08x\uff09} \u3002 \u3067\u5f97\u3089\u308c\u305f\u30a2\u30d7\u30ed\u30fc\u30c1 SUMA Trapezoidal \u95a2\u6570\u306e\u5834\u5408\u3001\u305d\u308c\u306f\u30ea\u30fc\u30de\u30f3\u306e\u5de6\u3068\u53f3\u306e\u5408\u8a08\u306e\u5e73\u5747\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 \u7a4d\u5206\u8a08\u7b97\u3068\u306e\u95a2\u4fc2 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u30c9\u30e1\u30a4\u30f3\u4e0a\u306e\u30ea\u30fc\u30de\u30f3\u306e\u5358\u6b21\u5143\u5408\u8a08\u306e\u5834\u5408  [ a \u3001 b ] {displaystyle {[a\u3001b]}} \u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u8981\u7d20\u306e\u6700\u5927\u30b5\u30a4\u30ba\u304c\u30bc\u30ed\u306b\u7e2e\u5c0f\u3055\u308c\u308b\u305f\u3081\uff08\u3064\u307e\u308a\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u6a19\u6e96\u306e\u5236\u9650\u306f\u30bc\u30ed\u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059\uff09\u3001\u4e00\u90e8\u306e\u95a2\u6570\u306f\u3059\u3079\u3066\u306e\u30ea\u30fc\u30de\u30f3\u5408\u8a08\u3092\u540c\u3058\u5024\u3067\u53ce\u675f\u3055\u305b\u307e\u3059\u3002\u3053\u306e\u5236\u9650\u5024\u306f\u3001\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u30c9\u30e1\u30a4\u30f3\u4e0a\u306e\u95a2\u6570\u306e\u5b9a\u7fa9\u3055\u308c\u305f\u30ea\u30fc\u30de\u30f3\u7a4d\u5206\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 \u222b a b f \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = \u30ea\u30e0 \u2016 d \u30d0\u30c4 \u2016 \u2192 0 \u2211 \u79c1 = \u521d\u3081 n f \uff08 \u30d0\u30c4 \u79c1 \u22c6 \uff09\uff09 d \u30d0\u30c4 \u79c1 {displaystyle int _ {a}^{b}\uff01f\uff08x\uff09\u3001dx = lim _ {| delta x | rightarrow 0} sum _ {i = 1}^{n} f\uff08x_ {i}^{star}\uff09\u3001delta x_ {i}}}}}}}} \u3002 \u6709\u9650\u30b5\u30a4\u30ba\u306e\u30c9\u30e1\u30a4\u30f3\u306e\u5834\u5408\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u8981\u7d20\u306e\u6700\u5927\u30b5\u30a4\u30ba\u304c\u30bc\u30ed\u306b\u7e2e\u5c0f\u3055\u308c\u308b\u5834\u5408\u3001\u3053\u308c\u306f\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u8981\u7d20\u306e\u6570\u304c\u7121\u9650\u306b\u306a\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u6709\u9650\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u5834\u5408\u3001Riemann\u306e\u5408\u8a08\u306f\u5e38\u306b\u5236\u9650\u5024\u306e\u8fd1\u4f3c\u3067\u3042\u308a\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u8584\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u6539\u5584\u3057\u307e\u3059\u3002\u6b21\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u6570\u3092\u5897\u3084\u3059\u65b9\u6cd5\u3092\u793a\u3059\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\uff08\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u8981\u7d20\u306e\u6700\u5927\u30b5\u30a4\u30ba\u304c\u7e2e\u5c0f\u3055\u308c\u307e\u3059\uff09\u304c\u3001\u66f2\u7dda\u306e\u4e0b\u306e\u300c\u9762\u7a4d\u300d\u306b\u8fd1\u3065\u304f\u306e\u304c\u826f\u304f\u306a\u308a\u307e\u3059\u3002 \u8d64\u3044\u95a2\u6570\u306f\u5747\u4e00\u306a\u95a2\u6570\u3067\u3042\u308b\u3068\u60f3\u5b9a\u3055\u308c\u308b\u305f\u3081\u3001\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u306e\u6570\u306f\u7121\u9650\u306b\u306a\u308b\u305f\u3081\u3001Riemann\u306e3\u3064\u306e\u5408\u8a08\u304c\u540c\u3058\u5024\u3067\u53ce\u675f\u3057\u307e\u3059\u3002 \u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u53c2\u7167 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u2191  Carmelo Sanchez Gonzalas\uff08\u7de8\uff09\u3002 \u300c4\u7a4d\u5206\u300d\u3002 \u5909\u6570\u306e\u7121\u9650\u8a08\u7b97 \u3002\u30de\u30b0\u30ed\u30a6\u30d2\u30eb\u3002 ISBN 978-84-481-5634-3 \u3002            (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/5560#breadcrumbitem","name":"Grittions Guived -Wikipedia\u3001The Free Encyclopedia"}}]}]