1. Use disks/washers to set. up an integral for the volume of the solid obtained by rotating the region bounded by f(x) = ¼x2 and g(x) = 5 - x2 about the x-axis. Do not evaluate the integral. Include a graph of the bounded region, with a labeled slice.
What are the dimensions (length and witdtth) of the slice?
2. Use cylindrical shells to set up an integral for the volume of the solid obtained by rotating the region bounded by y =1/x, x = 1, x = 2, y = 0 about the line x = 3. Do not evaluate the integral. Include a graph of the bounded region, with a labeled slice.
What are the dimensions (length and witdth) of the slice? What is the radius of rotation for the slice?
3. The integral
0∫Π/2 Π cos2 x dx
represents the volume of a solid obtained by rotating a bounded region R around a line.
a. List the equations that bound the region R.
b. What is the axis or line of rotation in Problem 3?
c. Sketch the graph of the region R. Include a slice that shows how the integral in Problem 3 was set up.