# Math Help - Antiderivative Question

1. ## Antiderivative Question

If f(x) = 4x - e - 0.5 x, and F(x) is an antiderivative function of f(x) with F(0) = 3, which of the following equals F(3) rounded off to two decimal places?

When I worked it out, I got 17.54, which is not right. Could someone explain? Thanks.

2. Hello vease1999
Originally Posted by vease1999
If f(x) = 4x - e - 0.5 x, and F(x) is an antiderivative function of f(x) with F(0) = 3, which of the following equals F(3) rounded off to two decimal places?

When I worked it out, I got 17.54, which is not right. Could someone explain? Thanks.
I assume you mean:
$f(x) = 4x -e^{-0.5x}$
in which case:
$F(x) = 2x^2+2e^{-0.5x}+c$

$F(0) = 2+c = 3$

$\Rightarrow c = 1$
$\Rightarrow F(3) = 18 + 2e^{-1.5}+1$
$= 19.45$ (2 d.p.)