Let f(x) be a function satisfyingf'(x)=f...

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

A

(a) `1/4(e-7)`

B

(b) `1/4(e-2)`

C

(c) `1/2(e-3)`

D

(d) `3-1/2e^(2)-3/2`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1) =a. Then , f (x) =

The value of int [f(x)g''(x) - f''(x)g(x)] dx is equal to

If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x then int_(cos theta)^(sec theta)f(x)dx=

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

If f(x) and g(x) are two functions with g (x) = x - 1/x and fog (x) = x^(3) -1/x^(3) then f(x) is

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

Let g(x) be the inverse of the function f(x), and f'(x)=1/(1+x^3) then g'(x) equals

If f (x) = 3x -1, g (x) =x ^(2) + 1 then f [g (x)]=