If `int_a^x ty(t)dt=x^2+y(x),` then find `y(x)`

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

A curve passing through (2,3) and satisfying the differential equation int_0^x ty(t)dt=x^2y(x),(x >0) is

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x) = int_(0)^(x) t cos t dt , then (df)/(dx)

If int_(0)^(x) f(t)dt=x^2+int_(x)^(1) t^2f(t)dt , then f'(1/2) is

If int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt , then the value of f(1) is

If y=int_(x^(2))^(x^(3))1/(logt)dt(xgt0) , then find (dy)/(dx)

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then