Prove the following
`int_(0)^(pi/2)sin^(3)xdx=2/3`

int_0^(pi/2) sin^(2)x dx =

Prove the following int_(0)^(1)sin^(-1)xdx=pi/2-1

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (b) int_(0)^(pi/2) cos^(2) xdx .

int_0^(pi/4) tan^(2)xdx

Prove the following int_(-1)^(1)x^(17)cos^(4)xdx=0

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (c) int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sin x) + sqrt(cos x))dx

Prove the following int_(1)^(3)(dx)/(x^(2)(x+1))=2/3+log2/3

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