Answer to Question #100066 in Calculus for Joseph Yep

Question #100066
1. Find the area of the regionenclosed by the curves x=y^2-2 and x=y.
1
Expert's answer
2019-12-09T11:54:26-0500

First let's find the intersection points of these curves

"y^2-2=y\\iff y^2-2-y=0"

"y=-1;\\quad y=2"

The area between these curves can be found as a Riemann integral

"S=\\left|\\int\\limits_{-1}^2(y^2-y-2)dy\\right|=\\left|\\left(\\frac{y^3}{3}-\\frac{y^2}{2}-2y\\right)_{-1}^2\\right|=\\frac{9}{2}"



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