Thread: finding the area

I am not sure what to do here for this problem.

Sketch the region enclosed by x+ y^2= 42 and x+y = 0. Decide whether to integrate with respect to x or y. Then find the area of the region.

Any help would be great

Originally Posted by mbrez88

I am not sure what to do here for this problem.

Sketch the region enclosed by x+ y^2= 42 and x+y = 0. Decide whether to integrate with respect to x or y. Then find the area of the region.

Any help would be great

First thing I would do is look at the graph and notice that it will be easier to do horizontal slicing.

Next find your points of intersection

$\displaystyle 42-y^2 = -y$

after set up your integral with your points of intersection

$\displaystyle \int (42 -y^2 + y)dy$