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Area Between Two Curves

  1. Nov 25, 2013 #1
    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. jcsd
  3. Nov 25, 2013 #2
    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.
     
  4. Nov 25, 2013 #3
    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!
     
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