For each of the problems below, complete the following: (a) sketch the region r. (b) draw a representative slice inside the region and sketch the rotation of the slice about the appropriate axis. (c) solve for the volume of the solid using the disk/washer method.
9. find the volume of the solid generate when the region bounded by the curves y=e^x, y=0, x=0, x=2 is revolved about the x-axis.
10. find the volume of the solid generated when the region bounded by the curves y=4x, y=x^3 in quadrant i is revolved around the x-axis.
11. find the volume of the solid generated when the region bounded by the curves x=.5y, x=y^(1/2) is revolved around the y-axis.
12. the region shown below is bounded by the graphs of y=secx, y=cosx, x=pi/3. find the volume of the solid obtained rotating this region about the x-axis.
13.the region shown below is bounded by the graphs of y=e^x, y=e^(x^2). find the volume of the solid obtained by rotating this region about the y-axis. ***set up integrals only**