# What is the net area between f(x) = x+8  and the x-axis over x in [2, 4 ]?

Jan 25, 2016

$22$

#### Explanation:

Using the rule:

$\int {x}^{n} \mathrm{dx} = \frac{{x}^{n + 1}}{n + 1} + C$

Find the antiderivative of the function:

$F \left(x\right) = \int \left(x + 8\right) \mathrm{dx} = {x}^{2} / 2 + 8 x + C$

To find the area, evaluate the integral from $F \left(2\right)$ to $F \left(4\right)$, which is equivalent to $F \left(4\right) - F \left(2\right)$.

$= {\left[{x}^{2} / 2 + 8 x\right]}_{2}^{4} = \left({4}^{2} / 2 + 8 \left(4\right)\right) - \left({2}^{2} / 2 + 8 \left(2\right)\right) = 22$