Consider the region R0 under the line y=x on the interval 0≤x≤3 and above the x-axis. The region is revolved about the horizontal line y=2, producing a solid.
a. Part 1: (a) Determine the x-value where the line y=x intersects the axis of rotation y=2.
b. Part 2: (b) Explain why the solid must be decomposed into two parts, one for 0≤x≤2 and one for 2≤x≤3, when writing an expression for its volume.
c. Part 3: (c) Write the two definite integrals with respect to x that, together, give the volume of the solid.
d. Part 4: (d) Evaluate the integrals and state the exact volume.