Math 252 Online Graded Assignment #1

It is essential to show all steps by hand. Also, if a method is prescribed, use only that method (no credit otherwise.)

Answers must be exact. Decimal approximations may not be given unless they are asked for

1. Let R be the region bounded by the graphs of and .

(i. 4 points) Determine the area of R.

(ii. 8 points) Determine the volume of the solid of revolution formed when R is revolved about the line y = 18.

2. Let P be the point (6,0), let Q be the point (0,4), and let R be the triangular region with vertices at P, Q, and the origin.

(i. 6 points) Determine the volume of the solid of revolution formed when R is revolved about the x-axis.

(ii. 8 points) Use the washer method (and no other method) to determine the volume of the solid of revolution formed when R is revolved about the line x = 7.

3. (8 points) A particle moves along the graph of the function at the constant rate of 3 units per minute. The particle starts at the point where x = 1 and travels in the direction of increasing x. After one hour, what is the x-value, rounded to the nearest hundredth, of the point of the location of the particle?

4. (4 points each) A force of 300 pounds compresses a 15-inch spring to a length of 5 inches.

(i.) Calculate the work done in compressing the spring an additional 3 inches.

(ii.) Calculate the work done in compressing the spring a total of 3 inches (from its natural length.)