If int(0)^(y)cost^(2)dt=int(0)^(x^(2))(s...

If `int_(0)^(y)cost^(2)dt=int_(0)^(x^(2))(sint)/tdt`, then prove that `(dy)/(dx)=(2sinx^(2))/(xcosy^(2))`.

A

`(2 sin x)/(x cos y)`

B

`(2 sin x ^(2))/(x cos y ^(2))`

C

`(2 sin x ^(2))/(x cos y)`

D

`(2 sin x)/(x cos y)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If int_0^ycost^2dt=int_0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)

int_(0)^(a) y^(2) dy

If f(x)=int_0^x(sint)/t dt ,x >0, then

int_(0)^(2) xsqrt(2-x)dx

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If y=int_0^xf(t)sin{k(x-t)}dt, then prove that ((dt^2y)/(dx^2))+k^2y=kf(x)

If int_0^y cos t^2\ dt = int_0^(x^2)\ sint/t \ dt , then dy/dx is equal to

int_(0)^(2) sqrt(2-x)dx .

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then