Page 88 - Calc for the Clueless

Volume of each section = (16y/3)∆y

Example 14—

2
Find the volume of the following figure: Again the base is bounded by y = ¼x and y = 4 in the x-y plane.
Sections perpendicular to the x axis are right isosceles triangles with one of the legs on the x-y plane.

Volume of each section = (8 - x + x /32)∆x
4
2

If you draw your pictures very carefully, this figure is symmetric with respect to the y axis. You can make the
problem easier by doubling the integral from 0 to 2. That is, y axis symmetry means