Math 10360 – Example Set 03A
1. Find the area bounded between the two curves x= sin yand x= sin 2yfor 0 ≤y≤π.
(You may use the identity sin2y= 2 sin ycos y.)
2. Find the volume of the solid shown below by integrating the area of vertical cross-section perpen-
dicular to the x-axis.
2
3
4
x
y
z
3. Consider a solid whose base is the region bounded by the lines y=x3,y= 8, and the y-axis. Find
the volume of the solid in each of the following cases:
a. The cross sections perpendicular to the y-axis are squares.
b. The cross sections perpendicular to the y-axis are rectangles of height √y.
c. The cross sections perpendicular to the y-axis are semicircles.
1
