Let f(x) and g(x) be two functions satisfying `f(x^(2))+g(4-x)=4x^(3), g(4-x)+g(x)=0`, then the value of `int_(-4)^(4)f(x^(2))dx` is :

If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) and g(x) + g(a-x) = 2 , then what is int_(0)^(a) f(x) g(x)dx equal to ?

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2). Then the value of the integral int_(0)^(1)f(x)g(x)dx, is

Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^2 . Then the value of integral int_0^1 f(x)g(x)dx is equal to (A) (e-2)/4 (B) (e-3)/2 (C) (e-4)/2 (D) none of these

If f(x) and g(x) are continuous functions satisfying f(x)=f(a-x) and g(x)+g(a-x)=2 then what is int_0^a f(x) g(x) dx equal to

f&g are two real valued continuous functions and let int g(x)dx=f^(-1)(x) and f(x)=x^(3)+x+sin pi x+2 then the value of int_(2)^(4)xy(x)dx is

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

Let f(x) and g(x) are 2 differentiable functions satisfying f(x)+3g(x)=x^(2)+x+62f(x)+4g(x)=2x^(2)+4 If J=int_(-(pi)/(4))^((pi)/(4))In(g(tan^(2)x)-f(tan x)-8)dx, then find the value of (3 pi In2)/(J)