(1) int_(0)^( pi/2)x^(2)sin^(2)xdx

Evaluate : (i) int_(0)^(1)sin^(-1)xdx , (ii) int_(1)^(2)(lnx)/(x^(2))dx , (iii) int_(0)^(1)x^(2)sin^(-1)xdx .

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

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

int_(0)^( pi/2)x sec^(2)xdx

Prove the following : 0 lt int_(0)^(pi//2)sin^(n+1)xdx lt int_(0)^(pi//2)sin^(2)xdx, n gt 1

Evaluate : int_(0)^(pi//2)sin^(8)xdx

int_(-pi//2)^(pi//2)sin^(7)xdx

3. int_(0)^( pi/2)sin^(2)x cos^(4)xdx

find the value of int_(0)^( pi/2)cos^(2)xdx

int_(0)^( pi/2)sec^(2)xdx