Find the Value of c for a 180 Area Enclosed by Two Parabolas

[jimen113]

[SOLVED] area problem

Homework Statement

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.

Homework Equations

Do I need to use the formula for the area of the circle?

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

 

[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.

 

[jimen113]

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

 

[Dick]

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

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

 

[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.

 

[cristo]

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.

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.

I've approved your attachment, anyway.

 

[jimen113]

Cristo,
Thanks for the feedback and the information on LaTex.