# Math Help - find the area of the region

1. ## find the area of the region

scetch the reason enclosed by x+y2=42 and x+y=0 Decide whether to integrate with respect to x or y. Then find the area of the region.

i tried solving for x but all i get is 7 can someone help im not sure how to integrate if i only get 1 point

2. We clearly need to integrate w.r.t. $y,$ so let's solve $42-y^2=-y\implies y^2-y-42=(y+6)(y-7)=0,$ so we integrate for $-6\le y\le7.$ Now put $f(y)=42-y^2$ and $g(y)=-y$ and see that it's $f(y)\ge g(y)$ and the integral which gives the area is $\int_{-6}^7\big(f(y)-g(y)\big)\,dy.$