Find the values of c such that the area of the region bounded by the parabolas

y = 4x^2 − c^2 and y = c^2 − 4x^2
is 256/3. (Enter your answers as a comma-separated list.)

1 answer

The parabolas intersect at x = -c/2 and c/2, so we want

∫[-c/2,c/2] (c^2-4x^2)-(4x^2-c^2) dx = 256/3
4c^3/3 = 256/3
c=4

naturally, c = -4 also works