04faex1v4 - Name TA Math 222 Prof Beck First Exam Fall 2004...

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Unformatted text preview: Name: TA: Math 222 Prof. Beck First Exam Fall 2004 1. Integrate ~t2cos t3—2 / < )dr sin2(t3 — 2) Math 222 Page 2 2. Integrate /sin4ycosSy dy Math 222 Page 3 3. Use the method of completing the square, along With a trigonometric substi— tution if needed, to evaluate each integral. /_3_X__dx Vx2+2x+5 Math 222 Page 4 4. Use integration by parts to evaluate / Math 222 I Page 5 5. Evaluate /sinycosyd 9 + cos4y y Math 222 Page 6 6. Evaluate this improper integral or Show that it diverges. 00 ; / 63—" cos x dx 0 Math 222 Page 7 7. Use the method of partial fraction decomposition to perform this integration. dx / 3x2 — 21x + 32 x3 ~ 8):2 + 16x Math 222 Page 8 8. Indicate Whether the given series converges or diverges. If it converges, find its sum. Hint: It may help you to write out the first few terms of the series. ...
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