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

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

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

Let f(x)=int_(0)^(x)(sin^(100)t)/(sin^(100)t+cos^(100)t)dt , then f(2pi)=

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

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

A function f is continuous for all x (and not everywhere zero) such that f^(2)(x)=int_(0)^(x)f(t)(cost)/(2+sint)dt . Then f(x) is

Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int_(0)^(x)e^(-t^(3)).f(x-t^(3))dt . Then find f(x) .

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt , then f(x+pi) is (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If F(x) =int_(x^(2))^(x^(3)) log t dt (x gt 0) , then F'(x) equals