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)`

If int_(0)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dt, then (dy)/(dx) is

int_(0)^(2 pi)[sin t]dt

If int _(0) ^(y) cos t ^(2) dt= int _(0) ^(x ^(2)) (sint)/(t ) dt then (dy)/(dx) is equal to

2int_(0)^(t)(1-cos t)/(t)dt

If int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2))sin^(2)tdt=0 , then (dy)/(dx) at x=y=1 is

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)

If y=int_(0)^(x)f(t)sin{k(x-t)dt, then prove that (dt^(2)y)/(dx^(2))+k^(2)y=kf(x)

If f(x)=int_0^x (sint)/(t)dt,xgt0, then

If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(dy)/(dx)=((1+y)cosx+ysinx)/(1+2y+cosx-sinx)