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 xe^(sin x)dx

I=int_(0)^(2 pi)cos^(-1)(cos x)dx

The value of I = int_(-1)^(1)[x sin(pix)]dx is (where [.] denotes the greatest integer function)

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)

If I_(1)=int_(0)^((pi)/(2))e^(sinx)(1+x cos x)dx and I_(2)=int_(0)^((pi)/(2))e^(cosx)(1-x sin x)dx, then [(I_(1))/(I_(2))] is equal to (where [x] denotes the greatest integer less than or equal to x)

If I_(1)=int_(0)^(pi//4)sin^(2)xdx and I_(2)=int_(0)^(pi//4)cos^(2)xdx , then

If I_(1)=int_(0)^(pi//4)sin^(2)xdx and I_(2)=int_(0)^(pi//4)cos^(2)xdx , then

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

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

If I_(1) = int_(0)^(pi//2)ln (sin x)dx , I_(2)=int_(-pi//4)^(pi//4)ln (sin x + cos x)dx , then :