int_(0)^( pi/2)cos xe^(sin m)dx

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

If I_(1)=int_(0)^( pi)x sin xe^(cos4x)dx , and I_(2)=int_(0)^( pi/2)cos xe^(cos4x)dx ,then the value of [(I_(1))/(I_(2))] is (where [.] denotes the greatest integer function)

int_(0)^( pi/2)|cos x-sin x|dx

If int_(0)^( pi)e^(sin x)dx=p. Then value of int_(0)^((pi)/(2))x cos xe^(sin x)dx is (A) (pi)/(2)e-p(B)(pi)/(2)e-2p (C) (pi)/(2)e-(p)/(2)(D)p

int_(0)^( pi)cos2x*log(sin x)dx

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

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

If l_1=int_1^x x sin x.e^sin dx and l_2=int_0^(pi/2) cos x.e^sin dx, then the value of [I_1/I_2] is (where [.] denotes greatest integer function)

int_(0)^(pi)(cos x)/(1-sin^(m)x)dx