14.Let f(x) be a function satisfying f '(x) = f(x)with f(0) = 1 and g be the function satisfyingf(x) + g(x) = x2. The value of the integralj f(x) g(x)dx isCase - e -(C){ e - 3)e - e2 - 3(B) e - e2 - 3Speed

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

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

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) .Prove that, int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)

If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x) , then the value of g ′ (1) is

If the function f(x)= x^(3)+e^(x/2) and g(x) = f^(-1)(x) then the value of g^(')(1) is

If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

Let f(x) = e^(x)g(x) , g(0)=2 and g (0)=1 , then find f'(0) .