(hat (:_(Y))int_(0)^( pi/2)(sin2 theta)/(sin^(4)theta+cos^(4)theta)d theta=(pi)/(2)

I=int_(0)^( pi/4)(sin2 theta)/(sin^(2)theta+cos^(4)theta)d theta

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

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

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

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

Show that int_(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2) theta)d theta = (pi)/(6)

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

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

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