2 calculus Q
2011-08-27 4:04 am
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回答 (2)
2011-08-27 4:25 am
✔ 最佳答案
1 ∫ x exp(x^2) dx= (1/2) ∫ exp(x^2) d(x^2)
= (1/2)exp(x^2) + C
2 ∫ cosx√sinx dx
= ∫ √sinx d(sinx)
= (2/3)(sinx)^(3/2) + C
2011-08-26 20:58:13 補充：
exp = exponential
2011-09-03 12:14 am
補充myisland兄答案)
如果唔熟integration的話，要做 substitution. 方法如下:
Let u = x^2 => du = 2*x dx => dx = du / (2*x)
int ( x*exp(x^2) ) dx = int ( x * exp(u) ) ( du / (2*x) ) = int exp(u)/2 du
如果唔熟integration的話，要做 substitution. 方法如下:
Let u = x^2 => du = 2*x dx => dx = du / (2*x)
int ( x*exp(x^2) ) dx = int ( x * exp(u) ) ( du / (2*x) ) = int exp(u)/2 du
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