`int_-pi^picos^8x`

Evaluate each of the following integral: int_0^picos^5x\ dx

Evaluate: int_(-pi)^pi(xsinx dx)/(e^x+1)

Evaluate: int_(-pi)^pi(xsinx dx)/(e^x+1)

Evaluate the following integral: int_0^picos2xlogsinx\ 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

Evaluate: int_(-pi)^pi(1-x^2)sinxcos^2xdx

1) int_(-pi/2)^pi sin^(-1) (sinx) dx 2) int_(-pi/2)^(pi/2) (-pi/2)/(sqrt(cos x sin^2 x)) dx 3) int_0^2 2x[x] dx

The value of int_(-pi)^(pi)(1-x^(2)) sin x cos^(2) x" dx" , is

int_(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dx has the value

int_(-pi//4)^(pi//4) e^(-x)sin x" dx" is