We first determine the points where the curves y = 8 - x^2 and y = x^2, meet.
8 - x^2 = x^2
=> x^2 = 4
=> x = 2 , x = -2
Now we find the integral of 8 - x^2 - x^2 between the limits x = -2 and x = 2
Int [ 8 - 2x^2 ]
=> 8x - 2x^3/3
Between the limits x = -2 and x = 2
8x - 2x^3/3 - 8x + 2x^3/3
=> 8*2 - 2*8/3 + 8*2 - 2*8/3
=> 32 - 32/3
=> 64/3
The area bounded by the curves is 64/3.
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