Answer to Question #100058 in Calculus for Yap

Question #100058
Find the area of the region enclosed by the curves x= y^2-2 and x=y.
1
Expert's answer
2019-12-09T11:50:43-0500

1) Limits of integration:


"y^2-2=y"

"D=(-1)^2-4(-2)=9=3^2"

"y_1=\\frac{1-3}{2}=-1"

"y_2=\\frac{1+3}{2}=2"

2)


"A=\\int_{-1}^2 (y-(y^2-2))dy"

"A=\\left(-\\frac{y^3}{3}+\\frac{y^2}{2}+2y\\right)_{-1}^2"

"A=\\left(-\\frac{2^3}{3}+\\frac{2^2}{2}+2(2)\\right)-\\left(-\\frac{(-1)^3}{3}+\\frac{(-1)^2}{2}+2(-1)\\right)"

"A=\\frac{9}{2}=4.5"


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