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Sierra's question at Yahoo! Answers regarding computing the area bounded by two functions

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MarkFL

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Feb 24, 2012
13,775
Here is the question:

Quick Calculus 1 question!?

The question is:

Find the are of the region lying to the right of x=y^2-5 and to the left of x=5-y^2

Please write down the steps!
Here is a link to the question:

Quick Calculus 1 question!? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.
 
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: sierra's question at Yahoo! Answers regarding computing the area bounded by two functions

Hello Sierra,

Let's look at a plot of the area $A$ in question:

sierra.jpg

As you can see, we can use the symmetry of the area to simply quadruple the first quadrant area shaded in red, to state:

\(\displaystyle A=4\int_0^{\sqrt{5}}5-y^2\,dy=4\left[5y-\frac{y^3}{3} \right]_0^{\sqrt{5}}=4\left(5\sqrt{5}-\frac{5\sqrt{5}}{3} \right)=\frac{40\sqrt{5}}{3}\)

To sierra and any other guests viewing this topic, I invite and encourage you to post other calculus questions here in our Calculus forum.

Best Regards,

Mark.