`int sin^(3) xsqrt(cos x)dx `का मान ज्ञात कीजिये ।

Explanation

माना `I = int sin ^(3) xsqrt(cosx)dx`
माना ` cos x = t^(2) rArr " " -sin xdx = 2t dt`
`rArr sin x dx = - 2t dt`
`therefore" "I=int sin^(2) xsqrt(cosx) sin x dx `
`= int (1-cos^(2) x)sqrt(cosx) sin x dx`
` = - int(1-t^(4)) t 2t dt = - 2 int (t^(2) - t^(6)) dt`
` = - 2((t^(3))/(3) - (t^(7))/(7)) = (2)/(7) (cos x)^(7//2) - (2)/(3)(cos x)^(x//2)`