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

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

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

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

If I=int_(0)^(2pi) sin^(2) x" dx" , then

int_(0)^(pi//2)sin x.sin 2x dx=

int_(0)^(pi//2) sin 2 x (tan x) dx=

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

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