# Area Between Two Curves

1. Nov 25, 2013

### MathewsMD

Find the values of c such that the area of the region bounded by the parabolas y = x2 - c2 and y = c2 - x2 is 576.

Attempt:

576 = -cc∫-x2 + c2 - (x2 - c2) dx

576 = 2-cc∫c2 - x2 dx

576 = c2x -(1/3)(x3) l0c *I know by symmetry that the area of 0 → c is half the area of -c → c

576 = c3 - (1/3)c3

576 = (2/3)(c3)

c ~ 9.52

This is the incorrect answer for c. I know there are other methods to solve this problem, but I am trying to answer this question using this strategy. Can anyone please point out the error in my work?
Thank you!

2. Nov 25, 2013

### Staff: Mentor

You did the integration incorrectly. First you lost your original factor of 2. Then, you lost another factor of 2 when you forgot to substitute the lower integration limit. Just redo the integration with more care, and you'll get the right answer.

3. Nov 25, 2013

### MathewsMD

Haha okay, I actually cancelled the factors out (I must have thought it was in the denominator for some reason). Thank you for finding it!