MHB Calc 1: Area Bounded by 2 Functions | Yahoo Answers

AI Thread Summary
The discussion focuses on finding the area bounded by the curves x = y^2 - 5 and x = 5 - y^2. A graphical representation is provided to illustrate the area of interest. The solution involves calculating the area in the first quadrant and then multiplying it by four due to symmetry. The area is computed using the integral A = 4∫(5 - y^2) dy from 0 to √5, resulting in A = (40√5)/3. Participants are encouraged to ask additional calculus questions in the linked forum.
MarkFL
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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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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:

https://www.physicsforums.com/attachments/768._xfImport

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

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

To sierra and any other guests viewing this topic, I invite and encourage you to post other calculus questions here in our http://www.mathhelpboards.com/f10/ forum.

Best Regards,

Mark.
 

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