AP Calculus
posted by Anon .
The base of a solid is bounded by y =x+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the yaxis is an equilateral triangle.

each crosssection has base 2x and altitude x√3
So, we want to add up all those triangles
v = ∫[a,3] 1/2 * 2x * x√3 dy
= √3 ∫[a,3] x^2 dy
But,
y = x + a
ya x
(ya)^2 = x^2
v = √3 ∫[a,3] (ya)^2 dy
and now it's cake, right?