1. The following calculators are allowed to be used on this examination: TI-81, 82, 83, 85, 86; Sharp EL-8200, EL-8200C. Any other calculator is subject to confiscation, and its user may be accused of cheating.
2. ONLY programs distributed in connection with MAT 131 and 132 may be stored in the calculators. Any other use of calculator memory to store information relevant to this examination will be considered cheating.

MAT 132
Calculus II
Midterm 1
October 12, 2000

Show all your work on these pages! Total score = 100

1. (20 points)
   
   • (a) Calculate the left-hand sum approximation to with n=3 equal subdivisions. Show all your work.

   • (b) Is this number an underestimate or an overestimate, compared with the integral? Explain why without using the ``exact'' numerical value of the integral.

2. (30 points) Calculate the following integrals. You must show work to earn a full grade.
   • (a)

   • (b)  , where n is a positive integer.

3. (30 points) Calculate the following improper integrals. You must show work to earn a full grade.
   • (a)  , where a is a number between 1 and 2.

   • (b)

4. (20 points) The base of a solid is a circular disk with radius 5. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypothenuse lying along the base.
   
   Calculate the volume of this solid.