Recitation 21 1. The base of a solid is the region between the curve y = 2sin x and the interval [ 0 , π ] on the x-­‐axis. Cross sections perpendicular to the x-­‐axis are equilateral triangles with bases running from the x-­‐axis to the curve as shown in #5, page 355. Find the volume of the solid. 2. Find the volume of the solid generated by revolving the region in the first quadrant bounded above by the parabola y = x 2 , below by the x-­‐axis, and on the right by the line x = 2 , about the y-­‐axis. 3. Use the shell method to find the volume of the solid generated by revolving the region bounded by y = x , y = − x / 2 , x = 2 about the y-­‐axis. 4. Use the shell method to find the volume of the solid generated by y = 3x , y = 0 , x = 2 about the line x = − 1 . 5. Find the length of the curve y =
x3
1
+
, 1 ≤ x ≤ 3 . 3 4x
6. Set up an integral for the length of the curve y = x 2 , − 1 ≤ x ≤ 2 .