Question

What is `f(x) = int x-e^(x-3)dx` if `f(0)=-2`?

Answer 1

`f(x)=x^2/2-e^(x-3)-2-e^(-3)`

Explanation:

using that

`int x-e^(x-3) dx=x^2/2-e^(x-3)+C`
we get that
`f(0)=e^(-3)+C=-2` so

`C=-2-e^(-3)`

we have used that

`int xdx=x^2/2+C_1`

`int e^(x-3)dx=e^(x-2)+C_2`