Question 16794
The function A(x) is obviously the area beneath the rectangle formed under the parabolic arch f(x) = 27-3x^2.  The rectangle has a width of 2x, and the height of the rectangle is y which equals 27-3x^2.  Since Area = width * length, 

A(x) = {{{2x*(27-3x^2)}}}.


This could also be expanded:

A(x) = {{{54x - 6x^3}}} or it could be factored completely:
A(x) = {{{6x*(9-x^2) }}}.


R^2 at SCC