Question

What is `f(x) = int x^3-2x+e^x dx` if `f(2) = 5`?

Answer 1

`f(x)=x^4/4-x^2+e^x-e^2+5`

Explanation:

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

`f(x)=x^4/4-x^2+e^x+C`

`f(2)=5=2^4/4-2^2+e^2+C` first equation

`5=4-4+e^2+C`

`C=5-e^2`

therefore from the first equation

`f(x)=x^4/4-x^2+e^x-e^2+5`