`int_((-pi)/(2))^((pi)/(2))sin^(7)x dx`

Evaluate : int_((pi)/(6))^((pi)/(3)) sin^(2) x dx

int_(-(pi)/(2))^((pi)/(2))(sin^(2)x)/(1+2^(x))dx=

int_(-(pi)/(2))^((pi)/(2))[sin|x|-cos|x|dx

int_(-(pi)/(2))^((pi)/(2))log((2-sin x)/(2+sin x))dx

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

Evaluate: int_(-pi//2)^(pi//2)sin^2x\ dx

int_(-pi/2)^(pi/2)sin^(9) x dx

1) int_(-(pi)/(2))^(pi)sin^(-1)(sin x)dx 2) int_(-(pi)/(2))^((pi)/(2))(-(pi)/(2))/(sqrt(cos x sin^(2)x))dx 3) int_(0)^(2)2x[x]dx

If A=int_((rho)/(2))^((pi)/(2))cos(sin x)dxB=int_(0)^((pi)/(2))sin(cos x)dx and C=int_(0)^((pi)/(2))cos(x)dx

Prove that : (i) int_(-pi)^(pi) x^(10) sin^(7) x dx =0 (ii) int_(-pi)^(pi) (sin^(25) x+x^(75))dx=0 (iii) int_(-pi)^(pi) e^(|x|) dx= 2 (e-1) (iv) int_(-pi//2)^(pi//2) sin^(9) x dx =0