Question

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

Answer 1

`f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+3.768`

Explanation:

First integrate to obtain `f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+c`
Then substitute `f(2)=3` to obtain `3=1/2e^3-1/3e^4+e^2+c`
Rearrange for c then evaluate: `c=3-1/2e^3+1/3e^4-e^2=3.768` (4s.f.)
Thus the original function is `f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+3.768`