If `f` is continuous function and `F(x)=int_0^x((2t+3)dotint_t^2f(u)d u)dt ,` then `|(F^(2))/(f(2))|` is equal to_____

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

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

Let f be continuous and the function g is defined as g(x)=int_0^x(t^2int_0^tf(u)du)dt where f(1) = 3 . then the value of g' (1) +g''(1) is

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

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

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Let f be a continuous function on [a , b]dot If F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)), then prove that there exist some c in (a , b) such that int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to