MATH 221 Review Exercises for Test 3

Part I – No Calculator

1. Find the most general anti-derivative of

2. Evaluate each of the following integrals:

Part II – Calculator allowed

1. . A rectangular poster is to have a total area of 600 square inches. The rectangular area of print is to have margins of 1 inch on the bottom and sides and 2 inches on the top. What is the maximum area possible for the print?

2. Find the area of the region bounded by .

3. Let R be the region bounded by x = 0, x = , y = 0, and y = cos(x). Find the volume of the solid that results when R is rotated around the x-axis and when it is rotated about the line x = -2.

4. Using an initial guess of 1, find the approximation to the solution of x³ + 2x² – 4 = 0 that results from applying Newton’s method twice.

5. Find the formula for the function f(x) that satisfies the given conditions: and f(0) = 2.