Calculus kinda with the area of two curves

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II don't even know where to start with this can anyone help?!?
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 270.

  • Calculus kinda with the area of two curves -

    the two curves intersect where

    x^2-c^2 = c^2-x^2
    that is, where x=±c

    The area is thus

    ∫[-c,c] (c^2-x^2)-(x^2-c^2) dx
    = 4∫[0,c] c^2-x^2 dx
    = 4(c^2 x - 1/3 x^3)[0,c]
    = 4(c^3 - 1/3 c^2)
    = 8/3 c^3

    8/3 c^3 = 270
    8c^3 = 30*3^3
    c = 3/2 ∛30

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