{"id":63919,"date":"2024-05-02T06:01:33","date_gmt":"2024-05-02T06:01:33","guid":{"rendered":"https:\/\/science-hub.click\/%E9%83%A8%E5%93%81%E3%81%AB%E3%82%88%E3%82%8B%E7%B5%B1%E5%90%88-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-05-02T06:01:33","modified_gmt":"2024-05-02T06:01:33","slug":"%E9%83%A8%E5%93%81%E3%81%AB%E3%82%88%E3%82%8B%E7%B5%B1%E5%90%88-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=63919","title":{"rendered":"\u90e8\u54c1\u306b\u3088\u308b\u7d71\u5408 – \u5b9a\u7fa9"},"content":{"rendered":"

\u6570\u5b66\u306b\u304a\u3051\u308b\u90e8\u5206\u7a4d\u5206\u3068\u306f<\/strong>\u3001\u8a08\u7b97\u3092\u7c21\u7565\u5316\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3001\u95a2\u6570\u306e\u7a4d\u306e\u7a4d\u5206\u3092\u4ed6\u306e\u7a4d\u5206\u306b\u5909\u63db\u3067\u304d\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/p>

\u6a19\u6e96\u7684\u306a\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002\u3053\u3053\u3067\u3001 f<\/i>\u3068g \u306f<\/i>\u9023\u7d9a\u5fae\u5206\u3092\u4f34\u3046 2 \u3064\u306e\u5fae\u5206\u53ef\u80fd\u306a\u95a2\u6570\u3067\u3042\u308a\u3001 a<\/i>\u3068b \u306f<\/i>\u5b9a\u7fa9<\/a><\/span>\u533a\u9593\u306e 2 \u3064\u306e\u5b9f\u6570\u3067\u3059\u3002 <\/p>

$$ {\\int_{a}^{b} f(x) g'(x)\\,\\mathrm dx = \\left[ f(x) g(x) \\right]_{a}^{b} – \\int_{a}^{b} f'(x) g(x) \\,\\mathrm dx} $$<\/div><\/dd><\/dl>

\u3042\u308b\u3044\u306f<\/p>

$$ {\\int u dv= uv-\\int v du} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001u \u306f\u88ab\u7a4d\u5206\u95a2\u6570<\/a><\/span>\u306e\u4e00\u90e8\u3092\u8868\u3057\u3001dv \u306f\u4ed6\u306e\u90e8\u5206\u3068\u7a4d\u5206\u5909\u6570<\/a><\/span>\u3092\u8868\u3057\u307e\u3059\u3002<\/p>

\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/a><\/span><\/span><\/h1>

\u3053\u306e\u5f0f\u306e\u8a3c\u660e\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059\u3002\u5b9f\u969b\u3001\u95a2\u6570 u \u3068 v \u306e\u7a4d\u306e\u5c0e\u51fa\u306e\u6027\u8cea\u304b\u3089\u76f4\u63a5\u5c0e\u304b\u308c\u307e\u3059\u3002

$$ {(u\\cdot v)’ = u’\\cdot v + u\\cdot v’} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>
$$ {\\int u'(x) v(x)\\,\\mathrm dx = \\int (uv)’ – \\int u(x) v'(x)\\,\\mathrm dx} $$<\/div><\/dd><\/dl>

\u3053\u308c\u306b\u3088\u308a\u3001\u4e0a\u8a18\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>

\u3053\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u306e\u8a18\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u884c\u3046\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 2 \u3064\u306e\u5fae\u5206\u53ef\u80fd\u306a\u95a2\u6570 u \u3068 v \u3092\u8003\u3048\u307e\u3059\u3002\u7a4d\u306e\u5c0e\u51fa\u898f\u5247\u306b\u3088\u308a\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>

$$ {\\frac {d(uv)}{dx}= u\\frac {dv}{dx}+v\\frac {du}{dx}} $$<\/div><\/dd><\/dl>

dx \u3092\u639b\u3051\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {d(uv)= u\\frac {dvdx}{dx}+v\\frac {dudx}{dx}} $$<\/div><\/dd>
d<\/i> ( u<\/i> v<\/i> ) = u<\/i> d<\/i> v<\/i> + v<\/i> d<\/i> u<\/i><\/span><\/dd><\/dl>

\u6b21\u306b\u3001\u5f0f\u3092\u6b21\u306e\u3088\u3046\u306b\u4e26\u3079\u66ff\u3048\u307e\u3059\u3002<\/p>

u<\/i> d<\/i> v<\/i> = d<\/i> ( u<\/i> v<\/i> ) \u2212 v<\/i> d<\/i> u<\/i><\/span><\/dd><\/dl>

\u6b21\u306b\u3001\u65b9\u7a0b\u5f0f\u3092\u7a4d\u5206\u3059\u308b\u3060\u3051\u3067\u3059\u3002 <\/p>

$$ {\\int u dv= \\int d(uv)-\\int v du} $$<\/div><\/dd><\/dl>

\u6b21\u306b\u3001\u4ee5\u4e0b\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p>

$$ {\\int u dv= uv-\\int v du} $$<\/div><\/dd><\/dl>

\u3053\u306e\u5f0f\u3092\u30af\u30e9\u30b9C<\/i> k<\/i> + 1<\/sup><\/span>\u306e\u95a2\u6570\u306b\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\int_{a}^{b} f(x) g^{k+1}(x)\\,\\mathrm dx = \\left[ \\sum_{n=0}^{k}(-1)^{n} f^{n}(x) g^{k-n}(x) \\right]_{a}^{b} + (-1)^{k+1} \\int_{a}^{b} f^{k+1}(x) g(x) \\,\\mathrm dx} $$<\/div><\/dd><\/dl>

\u5c0e\u51fa\u306b\u4f7f\u7528\u3055\u308c\u308b\u30eb\u30fc\u30eb\u306fLPET<\/i>\u30aa\u30fc\u30c0\u30fc\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u307e\u305a\u5bfe\u6570<\/strong>\u95a2\u6570\u3001\u6b21\u306b\u591a\u9805\u5f0f<\/strong>\u3001\u6307\u6570\u95a2\u6570<\/strong>\u3001\u305d\u3057\u3066\u6700\u5f8c\u306b\u4e09\u89d2\u95a2\u6570<\/strong>\u3067\u3059\u3002<\/p>

\u4f8b<\/span><\/h2>

\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046: <\/p>

$$ {\\int_{0}^{\\frac{\\pi}{3}} x\\cos (x) \\,\\mathrm dx} $$<\/div><\/dd><\/dl>

\u90e8\u54c1\u3054\u3068\u306e\u7d71\u5408\u306b\u3088\u308a\u3002\u3053\u306e\u305f\u3081\u306b\u3001\u79c1\u305f\u3061\u306f\u6b21\u306e\u3088\u3046\u306b\u5c0b\u306d\u307e\u3059\u3002<\/p>

f<\/i> ( x<\/i> ) = x<\/i><\/span> \u3001\u3064\u307e\u308af<\/i> ‘( x<\/i> ) = 1<\/span> \u3001<\/dd>
g<\/i> ‘( x<\/i> ) = cos( x<\/i> )<\/span> \u3001\u305f\u3068\u3048\u3070g<\/i> ( x<\/i> ) = sin( x<\/i> )<\/span>\u3068\u306a\u308a\u307e\u3059\u3002<\/dd><\/dl>

\u5f7c\u306f\u3084\u3063\u3066\u6765\u307e\u3059\uff1a <\/p>

$$ {\\int_{0}^{\\frac{\\pi}{3}} x\\cos (x) \\,\\mathrm dx = \\left[ f(x) g(x) \\right]_{0}^{\\frac{\\pi}{3}} – \\int_{0}^{\\frac{\\pi}{3}} f'(x) g(x) \\,\\mathrm dx} $$<\/div>
$$ {= \\left[x\\sin (x)\\right]_{0}^{\\frac{\\pi}{3}} – \\int_{0}^{\\frac{\\pi}{3}} \\sin (x) \\,\\mathrm dx} $$<\/div><\/dd>
<\/dd>
$$ {= \\frac{\\pi \\sqrt{3}}{6} – \\frac{1}{2}} $$<\/div><\/dd><\/dl><\/dd><\/dl>

\u6b21\u306e\u4e0d\u5b9a\u7a4d\u5206<\/a><\/span>\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <\/p>

$$ {\\int xe^x dx} $$<\/div><\/dd><\/dl>

\u90e8\u5206\u3054\u3068\u306b\u7d71\u5408\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>

u<\/i> = x<\/i><\/span>\u304a\u3088\u3073d<\/i> v<\/i> = e<\/i> x<\/i><\/sup> d<\/i> x<\/i><\/span><\/dd><\/dl>

\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

d<\/i> u<\/i> = d<\/i> x<\/i><\/span>\u304a\u3088\u3073v<\/i> = e<\/i> x<\/i><\/sup><\/span><\/dd><\/dl>

\u90e8\u5206\u3054\u3068\u306e\u7a4d\u5206\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <\/p>

$$ {\\int u dv= uv-\\int v du} $$<\/div><\/dd>
$$ {\\int xe^x dx= xe^x-\\int e^x dx} $$<\/div><\/dd><\/dl>

\u7a4d\u5206\u306e<\/a><\/span>\u8a08\u7b97\u304c\u306f\u308b\u304b\u306b\u7c21\u5358\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>

$$ {\\int xe^x dx= xe^x-e^x+C} $$<\/div><\/dd><\/dl><\/div>
\n\"\u90e8\u54c1\u306b\u3088\u308b\u7d71\u5408<\/figure>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u062a\u0643\u0627\u0645\u0644 \u0628\u0627\u0644\u062a\u062c\u0632\u0626\u0629 \u2013 arabe<\/a><\/li>
  2. \u0418\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430\u043d\u0435 \u043f\u043e \u0447\u0430\u0441\u0442\u0438 \u2013 bulgare<\/a><\/li>
  3. Parcijalna integracija \u2013 bosniaque<\/a><\/li>
  4. Integraci\u00f3 per parts \u2013 catalan<\/a><\/li>
  5. \u062a\u06d5\u0648\u0627\u0648\u06a9\u0627\u0631\u06cc \u0628\u06d5 \u0628\u06d5\u0634\u06a9\u0631\u062f\u0646 \u2013 sorani<\/a><\/li>
  6. Integrace per partes \u2013 tch\u00e8que<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u90e8\u54c1\u306b\u3088\u308b\u7d71\u5408 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n