Question

求各位大佬这个积分怎么求？

题目如图所示，要求有具体过程，谢谢！

Answer 1

y= sinx (0≤x≤π)
x= arcsiny
∫ (arcsiny) dy

=y.(arcsiny) - ∫ y/√(1-y^2) dy
=y.(arcsiny) +√(1-y^2) + C
Vy

=π∫ x^2 dy
=π∫(0->1) (π/2+arcsiny)^2 dy - π∫(0->1) (arcsiny)^2 dy
=π∫(0->1) [ (1/4)π^2+πarcsiny ] dy
=π [ (1/4)π^2.y +πy.(arcsiny) +π√(1-y^2) ] |(0->1)
=π [ (1/4)π^2 +(1/2)π^2 -π ]
=π [ (3/4)π^2 -π ]