Part B TIME: 60 MINUTES
No calculator is allowed for any of these problems.
If you finish Part B before time has expired, you may return to work on Part A, but you may not
use a calculator.
- Consider the first-quadrant region bounded by the curve the coordinate axes, and the line x
= k, as shown in the figure above.
(a) For what value of k will the area of this region equal π?
(b) What is the average value of the function on the interval 0 ≤ x ≤ k?
(c) What happens to the area of the region as the value of k increases? - The curve divides a first quadrant rectangle into regions A and B, as shown in the
figure.
(a) Region A is the base of a solid. Cross sections of this solid perpendicular to the x-axis are
rectangles. The height of each rectangle is 5 times the length of its base in region A. Find the
volume of this solid.
(b) The other region, B, is rotated around the y-axis to form a different solid. Set up but do not
evaluate an integral for the volume of this solid.