求不定积分,上限为π,下限为0,根号下（sint-sint的立方）dt,
问题描述：
求不定积分,上限为π,下限为0,根号下（sint-sint的立方）dt,
答
是求定积分!
I=∫√[sint-(sint)^3]dt=∫√{sint[1-(sint)2]}dt
=∫|cost|√sintdt
=∫cost√sintdt+∫(-cost)√sintdt
=∫√sintdsint-∫√sintdsint
=[(2/3)(sint)^(3/2)]-[(2/3)(sint)^(3/2)]
=2/3-(-2/3)=4/3.