Calculus kinda with the area of two curves
posted by Roni
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^2c^2 and y=c^2x^2 is 270.

Steve
the two curves intersect where
x^2c^2 = c^2x^2
that is, where x=±c
The area is thus
∫[c,c] (c^2x^2)(x^2c^2) dx
= 4∫[0,c] c^2x^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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