Calculus I, Math 251
Last One-hour Test name (10 points)
This heart warming fifty-minute test “covers” chapters six and nine of Calculus by Stewart.
Clearly indicate your answers. Except where indicated, each part of each problem is worth
five points. Pay attention to whether or not you need to evaluate the integrals.
1. Find the area between the curves: y = sec2x, y = 0, x = 0 and x = π/4.
a. The integral:
b. The exact answer:
c. What is the average value of sec2x on this interval?
2. Find the area between the curves: x = y3 − y and x = y4 − 1.
a. The integral:
b. The exact answer:
3. The base of an object S is the area between y = 4 − x2 and the x-axis. Cross-sections
perpendicular to the x-axis are circles. Set up an integral to evaluate the volume of the
solid S. (Do not evaluate it.)
