MAT 220 – 001

Fall 2000

Test One

Show all work.

On the integration problems, show the detail of each step.

Some stuff:

The test:

1. (10 points) Integrate . Show all steps.

2. (15 points) Integrate . Show all steps.

3. (10 points) Use Simpson’s rule with n = 10 to approximate the integral

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4. (10 points) Set up an integral that represents the area of the surface generated by revolving the portion of the curve about the y-axis. You may use your calculator to determine the value of the integral.

5. (10 points) Eliminate the parameter and find a Cartesian equation of the curve

6. (10 points) Consider the curve .

6a. Find in terms of t.

6b. Find in terms of t.

7. (10 points) Find equations for the tangent lines to the curve at the points where the curve crosses the x-axis.

8. (15 points) Set up an expression that represents the area that is common to the curves and . You may use your calculator to determine the value of the integral.

9. (10 points) Set up an integral that represents the length of the arc . You may use your calculator to determine the value of the integral.