推 aether982:多謝啦!!! 又麻煩你一次了!!! 04/06 01:31
推 finalgod:本來也沒想到竟然會有這樣的限制^^ 04/06 01:36
※ 引述《aether982 (Let go of me)》之銘言：
: 要什麼情況之下
: d[S f(x) dx]/dx = S [df(x)/dx] dx
: 才會成立呢??
不定積分後者會多1個常數C
d[∫f(x) dx]/dx = ∫[df(x)/dx] dx + C
若是定積分範圍就用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
積分範圍一樣的看來也要有所限制XD
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