From f1a8f3abfed2b10020b42c0976cae68b4db557a5 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Sun, 25 Jul 2021 23:27:50 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E7=A7=AF=E5=88=86?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...ntegal-of-functions-of-single-variable.pdf | Bin 291307 -> 198576 bytes ...ntegal-of-functions-of-single-variable.tex | 2 +- .../derivatives-and-differential.pdf | Bin 143194 -> 143233 bytes .../derivatives-and-differential.tex | 2 +- ...efinite-integral-and-definite-integral.pdf | Bin 297069 -> 204559 bytes ...efinite-integral-and-definite-integral.tex | 4 +++- 6 files changed, 5 insertions(+), 3 deletions(-) diff --git a/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf b/advanced-math/exercise/4-integal-of-functions-of-single-variable/integal-of-functions-of-single-variable.pdf index 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f@9F96V(8@J;bdwC!@|wM%*+i#PA(=d4)ebNpNhBP diff --git a/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex b/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex index b184c00..8941a86 100644 --- a/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex +++ b/advanced-math/knowledge/4-indefinite-integral-and-definite-integral/indefinite-integral-and-definite-integral.tex @@ -597,6 +597,8 @@ $\int_0^\pi xf(\sin x)\,\textrm{d}x=-\int_\pi^0(\pi-t)f(\sin(\pi-t))\,\textrm{d} 当积分区间为无穷区间,或被积函数为无界函数,那么定积分就无法“定”下来,所以这种积分就是反常积分。 +对于无穷区间的反常积分首先求出原函数,然后代入上下限。 + \subsubsection{无穷区间} 设函数$f(x)$在区间$[a,+\infty)$上连续,任取$t>a$,做定积分$\int_a^tf(x)\,\textrm{d}x$,对这种变上限积分的极限$\lim\limits_{t\to+\infty}\int_a^tf(x)\,\textrm{d}x$就是$f(x)$在无穷区间$[a,+\infty)$上的反常积分,记为$\int_a^{+\infty}f(x)\,\textrm{d}x$。 @@ -623,7 +625,7 @@ $\int_0^\pi xf(\sin x)\,\textrm{d}x=-\int_\pi^0(\pi-t)f(\sin(\pi-t))\,\textrm{d} 对于无界函数的反常积分要求的就是$\lim\limits_{x\to a}f(x)$。 -\subsection{* 反常积分的判敛} +% \subsection{* 反常积分的判敛} \subsection{不定积分与定积分的区别与联系}

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