Calculus 2

Final Exam

2 MAY 01

1.)

2.)

3.) ò sin³x cos²x dx

4.)

5.) Consider the following series.

a.) Find the sum of the first 90 terms of the series. Feel free to use your calculator.

b.) Determine convergence or divergence for the series. If it converges, find its sum.

6.) Determine convergence (absolute or conditional) or divergence for the given series.

7.) Determine convergence or divergence for the given sequence. If the sequence converges, give its limit.

8.) Consider the region bounded by f(x) = x², y = 0, x = 2. Suppose the region is revolved around the line x = 3. Find the volume of the resulting solid. (Exact answer only.)

9.) Find the exact area bounded by the curves f(x) = x² and g(x) = 2x + 3.

10.)

Part 2 - Open Book

11.) Do #44 on page 453. You can use the following picture to help.

12.) Find the centroid of the region under the curve y = cos 2x from x = 0 to x = p. Exact answers.

13.) Use the table of integrals in the back of the book to do the following. Be sure to tell which formula you used.

14.) Set up the integral (AND USE YOUR CALCULATOR TO EVALUATE IT) to find the arc length of the curve y = sin 3x, x = 0 to x = 2p.

15.) Use the fact that sin 2x = 2 sin x cos x to find the Maclaurin series for f(x) = sin x cos x.

16.) Do #2 on page 512.

17.) Convert the point (-3, -3) to polar coordinates. Exact answers only.

18.) Graph r = 4 sin (3q). Label the angles and distances at the center of each leaf. Use exact values.

19.) Graph x = cos t - sin (t/3), y = 2 cos t + sin (t/3).

20.) Set up the integral (AND USE YOUR CALCULATOR TO EVALUATE IT) to find the surface area of the surface generated by revolving the curve y = sin x, x = 0 to x = p, around the line y = 4.