Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. x = 45 − 5y^2, x = 5y^2 − 45

Question

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle.

x = 45 − 5y²,    x = 5y² − 45

Answer 1

If you are not experienced with plotting on a graph, spend some time with a tool such as desmos:

https://www.desmos.com/calculator

This is a very powerful tool for visualizing the properties of various equations.

Regardless, always start a plot with 1 or 2 "anchor" points--eg the value of y when x = 0 (or vice-versa). Also, look at the behavior when one of the variables gets very large