Area problem

1. Apr 27, 2008

jimen113

[SOLVED] area problem

1. The problem statement, all variables and given/known data
find c>0 such that the area of the region enclosed by the parabolas y=x^2-c^2 and y=c^2-x^2 is 180.

2. Relevant equations
Do I need to use the formula for the area of the circle?

3. The attempt at a solution

I graphed both functions and I can clearly see that they are symmetrical parabolas one upward and one downward parabolas.
Then, I tried to work backwards and find the integral. $$\int$$(2x$$^{}2$$-2c$$^{}2$$)dx
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 27, 2008

Dick

That's a good start. But I would take y on the upper parabola minus the y on the lower parabola, so I get 2c^2-2x^2. Now all you need is limits on the integral. Any ideas from your graph? No, this has nothing to do with circles.

3. Apr 27, 2008

jimen113

from the graph, when x=-/+.21 y=0 (point of intersection)

4. Apr 27, 2008

Dick

Only if c=0.21, right? If you don't know C you'd better just say x=+/-C.

5. Apr 29, 2008

jimen113

Thanks for your help. I'm trying to post the solution using math type, it's not working. However, if you're interested in the solution, please see attachment. And if anyone knows how to post from math type to this forum please help me out. I've tried copy and paste..it does not work.

Attached Files:

• webwork 10.doc
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6. Apr 29, 2008

cristo

Staff Emeritus
I don't know what mathtype is, but you could use LaTeX. There is a thread somewhere, probably in feedback, telling you how to get started.