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_0^1f(x) g(x) dx`, is

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

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to

Let f(x) be a continuous function on [0,4] satisfying f(x)f(4-x)=1. The value of the definite integral int_(0)^(4)(1)/(1+f(x))dx equals -

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f(x) be a function satisfying f'(x) = f(x) and f(0) = 2. Then int(f(x))/(3+4f(x))dx is equal to