A differentiable function y = g(x) satisfies `int_0^x(x-t+1) g(t) dt=x^4+x^2` for all `x>=0` then y=g(x) satisfies the differential equation

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

A differentiable function satisfies f(x)=int_(0)^(x){f(t)cost-cos(t-x)}dt. Which is of the following hold good?

Let g:R rarr R be a differentiable function satisfying g(x)=int_(0)^(x)(g(t)*cos t-cos(t-x))dt for all x in R Find number of integers in the range of g(x)