Posted by Anon on Sunday, March 16, 2014 at 6:13pm.
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.

AP Calculus  Steve, Monday, March 17, 2014 at 12:00am
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?
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