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

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

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

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

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

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

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

int_(0)^( pi/4)sec xdx

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

(i) int_(0)^(pi//2) x sin x cos x dx (ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx

int_0^(pi/2) cos^5xdx