# Question #34974

Aug 15, 2017

Here is the region. To make the graph easier to see, I have scaled the $x$ axis by a factor of $\frac{1}{9}$. The "real" $x$ intercepts are at $- 45$ and $45$.
Although we could draw the typical rectangle vertically and integrate with respect to $x$, I would prefer to draw the rectangle horizontally and integrate with respect to $y$
The area is ${\int}_{-} {3}^{3} \left(\left(45 - 5 {y}^{2}\right) - \left(5 {y}^{2} - 45\right)\right) \mathrm{dy}$.