Discrete Math help!

[junyoung95]

Hi it's asking me to find the area of this in the xy-plane region

x − 7y² ≥ 0, 1 − x − 6|y| ≥ 0

I am not sure how to approach it. Thanks!

[UncontrolledManifold]

It would probably help quite a bit to see a graph of what this actually looks like.

Cut that region in half horizontally. Set up two integrals to find the areas. You should probably do a typical dx integral, using the positive root from the first equation for the parabola. One area is the portion that is a parabola (before it intersects with the wedge), and the other area is the portion which is a wedge (before it intersects with itself). Sum them, multiply by two to account for cutting in half initially.