`I=int_0^(pi//4)(sin2theta)/(sin^2theta+cos^4theta) \ d theta`

int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta

int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then

Consider int_0^(pi//2)(sin2thetad theta)/(sin^4theta+cos^4theta) Show that value of the integral is pi/2 .

int_(0)^((pi)/(2))(sin^(3)theta)/(sin^(3)theta+cos^(3)theta)d theta

Evaluate int _(0)^(pi//2) (cos^(4) theta)/(sin^(4) theta + cos^(4) theta)d theta