^{2}- c

^{2}and y = c

^{2}- x

^{2}is 576.

Attempt:

576 =

_{-c}

^{c}∫-x

^{2}+ c

^{2}- (x

^{2}- c

^{2}) dx

576 = 2

_{-c}

^{c}∫c

^{2}- x

^{2}dx

576 = c

^{2}x -(1/3)(x

^{3}) l

_{0}

^{c}*I know by symmetry that the area of 0 → c is half the area of -c → c

576 = c

^{3}- (1/3)c

^{3}

576 = (2/3)(c

^{3})

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!