Question

Find the net area and the area of the region bounded by y=8cos and the x-axis between x=-pi/2 and x=pi

Answer 1

The net area of the region in relation to the x-axis, is just the integral at those bounds, thus

$\bf \displaystyle \int\limits_{-\frac{\pi }{2}}^{\pi }~8cos(\theta )\cdot d\theta \implies 8\int\limits_{-\frac{\pi }{2}}^{\pi }~cos(\theta )\cdot d\theta \\\\\\ \left. 8sin(\theta )\cfrac{}{} \right]_{-\frac{\pi }{2}}^{\pi }\implies [8sin(\pi )]~-~\left[8sin\left(-\frac{\pi }{2} \right) \right]\implies [0]-[-8]\implies 8$