Question

Question #34974

Answer 1

Please see below.

Explanation:

Here is the region. To make the graph easier to see, I have scaled the `x` axis by a factor of `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 ((45-5y^2)-(5y^2-45)) dy`.

There is some symmetry we could use if we wish to.