Question

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

Answer 1

`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.!