Find the area of the region between the curves x=4-y² and x=-3y

I keep getting 56/3 but that doesnt match any other answer. can someone help me out?

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- Oct 4th 2010, 06:52 PMandrewho93Area between curves
Find the area of the region between the curves x=4-y² and x=-3y

I keep getting 56/3 but that doesnt match any other answer. can someone help me out? - Oct 4th 2010, 07:29 PMtonio

First, I think it'll be much easier to represent both as functions of x: $\displaystyle y=4-x^2\,,\,y=-3x$

These two funtions intersect at $\displaystyle x=-1,\,4\Longrightarrow$ the wanted area is the integral:

$\displaystyle \int\limits^4_{-1}(4-x^2+3x)dx$ (why? Chech that the parabola lies above the line in the integration interval...)

I got as answer $\displaystyle \frac{125}{6}=20.833333$

Tonio