The figure above shows the graph of and the graph of . What is the area of the shaded region?

Let be the volume of the solid generated by revolving the region enclosed by , the -axis, ; about the -axis. Then is

Let be the volume of the solid generated by revolving the region enclosed by , ; about . Then is

The figure above shows a shaded region enclosed by and . What is the volume of the solid created when the region is rotated about the line ?

Let be the volume of the solid generated by revolving the region enclosed by , ; about -axis. Then is

The figure above shows a shaded region enclosed by , , and . Using the shell method, what is the volume of the solid generated by revolving the region about the x-axis?

Let be the volume of the solid which lies between planes perpendicular to the -axis from to . The cross sections of this solid perpendicular to the -axis run from to and they are squares with bases in the -plane. Then is

A solid has a base that is the region enclosed by and the x-axis shown in the figure above. The cross sections perpendicular to the y-axis are semicircles. What is the volume of the solid?

The arc length of for is