Originally Posted by

**KDonicki** I have two problems I need help on:

1. Find the area of the region lying to the right of x=(y^2)-5 and the left of x=3-(y^2).

I determined that the limits of integration would be [-5, 3] and then I tried to integrate ((y^2)-5)-(3-(y^2)), but I keep getting a REALLY large unrealistic number,

First have you sketched the curves?

Code:

EuMathT code to sketch curves
>y=-6:0.1:6;
>
>x1=y^2-5;
>x2=3-y^2;
>
>
>xplot(x1,y);
>hold on;plot(x2,y);
>hold off
>

Sketch attached.

So you see that you need to integrate:

$\displaystyle \int_{y=-2}^2 (y^2-5)-(3-y^2) dy$

RonL