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

For x in R, x != 0, if y(x) differential function such that x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt, then y(x) equals: (where C is a constant.)

If f(x)=int_0^x tf(t)dt+2, then

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find 9f'(4)

If y = int_(1)^(x) xsqrt(lnt)dt then find the value of (d^(2)y)/(dx^(2)) at x = e

If {F(x)}^(101)=int_0^x(F(t))^(100)(dt)/(1+sint), then find F(x)

Let f(x) = int_(0)^(x)(t-1)(t-2)^(2) dt , then find a point of minimum.

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

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

If g(x) is continuous function in [0, oo) satisfying g(1) = 1. If int_(0)^(x) 2x . g^(2)(t)dt = (int_(0)^(x) 2g(x - t)dt)^(2) , find g(x).

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.