What is F(x) = int x^2+e^(4-2x) dx if F(0) = 1 ?

1 Answer
Sep 21, 2016

F(x)=x^3/3-e^4/2(e^(-2x)+1)+1.

Explanation:

F(x)=int(x^2+e^(4-2x))dx=intx^2dx+inte^(4-2x)dx

rArr F(x)=x^3/3+e^(4-2x)/-2+C

To determine C, we use the cond. F(0)=1

rArr 0^3/3+e^(4-0)/-2+C=1.

rArr C=1-e^4/2.

Sub.img, in F(x), we get,

F(x)=x^3/3-e^(4-2x)/2+1-e^4/2, i.e., x^3/3-e^4/2(e^(-2x)+1)+1.

Enjoy Maths.!