MATH 222 Test 2 Name________________

Instructions: Answer all the questions on the test and show all your work. You may use the calculator for all questions.

1. Using an appropriate substitution (write down the substitution) change the following integral to an integral of the product of trigonometric functions. Do not evaluate the integral further. (10)

2. Using an appropriate substitution (write down the substitution) change the following integral to an integral of the product of trigonometric functions. Do not evaluate the integral further. (10)

3. Given the following partial fraction expansion determine the constants A, B, C, and D.

(12)

4. The point P is given as in x-y coordinates. Write P in polar coordinates in three different ways, one of which has r negative. (12)

5. Write as an equation in x-y coordinates. (8)

6. Find the area enclosed by the curve . (12)

7. Eliminate the parameter from the parametric equations:

(10)

8. a) Find all points on the graph of the curve given by at which the tangent lines are either horizontal or vertical. Express these points in x-y coordinates. (10)

b) This curve crosses itself to enclose a region in the plane. Find the area of this enclosed region. (10)

9. Find the length of the graph of (10)