作者finalgod (0_o安ㄚ)
看板trans_math
标题Re: [微积] 积分跟微分的顺序
时间Thu Apr 6 01:23:37 2006
※ 引述《aether982 (Let go of me)》之铭言：
: 要什麽情况之下
: d[S f(x) dx]/dx = S [df(x)/dx] dx
: 才会成立呢??
不定积分後者会多1个常数C
d[∫f(x) dx]/dx = ∫[df(x)/dx] dx + C
若是定积分范围就用Leibniz's Rule
M(x)
d[∫ f(x) dx]/dx = f[M(x)]×(d M(x)/dx)–f[N(x)]×(d N(x)/dx)
N(x)
M(x)
∫ [df(x)/dx] dx = f[M(x)]–f[N(x)]
N(x)
d M(x)/dx = 1 → M(x) = x + c1
d N(x)/dx = 1 → N(x) = x + c2
x+c1 x+c1
d[∫ f(x) dx]/dx = ∫[df(x)/dx] dx
x+c2 x+c2
积分范围一样的看来也要有所限制XD
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1F：推 aether982:多谢啦!!! 又麻烦你一次了!!! 04/06 01:31
2F：推 finalgod:本来也没想到竟然会有这样的限制^^ 04/06 01:36