## Math 121 - Chapter 6 Exam

1. Write the integral(s) necessary to find the area between the curves. Do NOT evaluate the integral(s).
2. Setup the integral necessary to find the arc length of a parametric curve. Do NOT evaluate the integral.
3. Sketch the region enclosed by the curves and find its area. Two parts. Look at problems 6.1.7-14.
4. A solid is described to you. Find the cross sectional area of a slice. Find the volume of the solid. Multiple choice. Look at the explanation of volumes by slicing in the text in section 6.2.
5. Sketch the region described in the x-y plane and then find the volume when the region is rotated about one of the axes. Four parts. Identify the method used to find the volume. You may use the disk method, washer method, or cylindrical shell method, but you must use each method at least once. Look at problems 6.2.5-20 and 6.3.5-14.
6. Find the exact arc length of the curve over the given interval. Two parts. Look at problems 6.4.3-8.
7. Find the surface area of revolution when the curve is rotated about the indicated axes. Two parts. Look at problems 6.5.1-8.
8. Work problem - springs. Look at problems 6.6.4-7.
9. Variable work problem. Look at problems 6.6.8-17.
10. Work energy problem. Look at problems 6.6.21-23.
11. Find the fluid force on the submerged surface. Look at problems 6.7.3-8.

### Notes:

• ĽSome of the problems are directly from the textbook.
 # 1 2 3 4 5 6 7 8 9 10 11 Total Pts 5 5 12 6 24 12 12 6 6 6 6 100