" Iet "l_(i)=int_(0)^(oo)cos((2 pi)/(3)sin^(2)x)dx" and "I_(3)=int_(0)^(oo)cos((pi)/(3)sin x)dx" then the value of "(t_(2))/(r_(1))" equals "

u,=int_(0)^((pi)/(2))cos((2 pi)/(3)sin^(2)x)dx and v,=int_(0)^((pi)/(2))cos((pi)/(3)sin x)dx

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

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

Find I=int_(0)^((3 pi)/(2))cos^(4)(3x)sin^(2)(6x)dx

If I=int_(0)^((3 pi)/(5))(1+x)sin x+(1-x)cos x)dx then value of (sqrt(2)-1)I is

If I_(I)=int_(0)^( pi/2)cos(sin x)dx,I_(2)=int_(0)^((pi)/(2))sin(cos x)d, and I_(3)=int_(0)^((pi)/(2))cos xdx then find the order in which the values I_(1),I_(2),I_(3), exist.

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