Question

求定积分∫（0,π） √（sin^3 x-sin^5 x)dx

Answer 1

I=∫√（sin^3 x-sin^5 x)dx (0,π)= ∫ sinx√(sinx-(sinx)^2 ) dxlet a = sinxda = cosx dxx=0,a=0x=π,a =1I= ∫ a √ (a- a^2) da/( √(1-a^2) (0,1)= ∫ a^(3/2) da (0,1)= (2/5)[a^(5/2)] (0,1)=2/5