Question

这个积分怎么算，给详细的步骤给我

Answer 1

∫(0->π) (sint)^3 dt
=-∫(0->π) (sint)^2 dsint
=- (1/3)[ (sint)^3 ]|(0->π)
=0

追问

答案不是等于0，答案好像要根据对称性来分成0->π/2来解，为什么sint的积分可以变成-dsint的？

追答

不好意思
∫(0->π) (sint)^3 dt

=-∫(0->π) [1- (cost)^2] dcost
= -(1/3)[ cost - (1/3)(cost)^3 ]|(0->π)
=-(1/3)[ ( -1 +1/3) - (1 - 1/3) ]
=-(1/3) (-4/3)
=4/9