What is F(x) = int 3x^2+e^(2-2x) dx if F(0) = 1 ?

1 Answer
Jan 12, 2017

F(x) = x^3 +e^2/2 (1-e^(-2x)) +1

Explanation:

int 3x^2+e^(2-2x) dx = 3intx^2 dx+ e^2 int e^(-2x) dx

= 3*x^3/3 + e^2 int e^(-2x) dx

int e^(-2x) dx = -1/2e^(-2x)

:. F(x) = x^3 - e^2/2 * e^(-2x) +C

Since F(0) =1

0^3 - e^2/2 * e^(-2*0) +C =1

-e^2/2 *1 +C =1

C= 1+e^2/2

F(x) = x^3 - e^2/2 * e^(-2x) +1+e^2/2

= x^3 +e^2/2 (1-e^(-2x)) +1