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 470 . What does c=?

Answer 1

Make a sketch.

The area runs from x=-c to x=c.

If you simply integrate you will get 0 because the area is symmetric about the x axis.

It is also symmetric about the y axis.

To get the actual area (rather than the algebraic area), it will be 4 times the

integral from 0 to c of x²-c² which will be a function of c.

Set that function equal to 470 and solve it.

If the function turns out to be a cubic, solve it graphically.