`I=int_(0)^( pi/2)x^(2)cos^(2)x*dx`

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

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

Evaluate the following : int_(0)^(pi//2)(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)

int_(0)^( pi)(dx)/(1+cos^(2)x)

(i) int_(0)^( pi)x cos^(2)xdx

int_(0)^(pi//4) cos^(2) x dx

int_(0)^(pi/2) (cos^(2)x dx)/(cos^(2)x+4 sin^(2)x)

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

If int_(0)^(pi)((x)/(1+sinx))^(2) dx=A, then the value for int_(0)^(pi)(2x^(2). cos^(2)x//2)/((1+ sin x^(2)))dx is equal to

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx