Question

What is `f(x) = int e^(2x)-2e^x+3x dx` if `f(4 ) = 2`?

Answer 1

`f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22`

Explanation:

`f(x) = int (e^(2x) - 2e^x + 3x)dx`
`:. f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + c`

Now `f(4)=2`
`:. e^8/2 - 2e^4 + (3(16))/2 + c = 2`
`:. e^8/2 - 2e^4 + 24 + c = 2`
`:. c = 2e^4 - e^8/2 - 22`

Hence, `f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22`