# What is the net area between f(x) = cosx  and the x-axis over x in [0, 3pi ]?

Aug 11, 2016

$0$

#### Explanation:

This is expressed as:

$A = {\int}_{0}^{3 \pi} \cos \left(x\right) \mathrm{dx}$

The antiderivative of $\cos \left(x\right)$ is $\sin \left(x\right)$:

$A = {\left[\sin \left(x\right)\right]}_{0}^{3 \pi} = \sin \left(3 \pi\right) - \sin \left(0\right) = \sin \left(\pi\right) - \sin \left(0\right) = 0$
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