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## Homework Statement

Consider the region enclosed by the curves x=2-y^2 and y=-x

Write a single integral that can be used to evaluate the area of the region. Find this area. Your answer should be a fraction reduced to its lowest terms.

## Homework Equations

NA

## The Attempt at a Solution

First, I graphed them and found the intersection points. The graphs intersect at the points (-2,2) and (1,-1). To write the integral, I decided to integrate with respect to y, I have:

Integral from y=2 to y=-1 of (-y)-(2-y^2)dy

Solving this, I got that the area should be 1.5, however I was told the answer is 4.5. Any ideas where I went wrong?

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