`int_(0)^(pi//2) sqrt(cos x) sin ^(3) x" "dx=`

Evaluate: \int_{0}^(2pi) sqrt cos x sin^3 x dx

If int_(0)^(pi//2) sin^(4) x cos^(2)x dx = (pi)/(32) then int_(0)^(pi//2) cos^(4) x sin^(2) x dx=

Compute the integrals : (a) int_(0)^(pi//2) sin 2x dx , (b) int_(pi//6)^(pi//2) (cos x)/(sin^(3) x) dx (c) int_(0)^(1) (dx)/( sqrt(16 - x^(2)))

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

int_(0)^(pi//2) x sin x cos x dx

int_(0)^(pi//2) x sin x cos x dx

int_(0)^(pi//6) (sin x) /(cos^(3)x) dx is

int_(0)^(pi//2) sqrt(sin x)/(sqrt(sin x ) + sqrt( cos x)) dx =