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# A3 - 1 Z x 2 sin xdx 2 Z arcsin(2 x dx 3 Z x 3 x-2 2 dx 4 Z...

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Math 128 ASSIGNMENT 3: Integration strategy Winter 2012 Due at 8:25 am on Wednesday, January 25 th in the correct drop slot across from MC4066 or in class depending on your instructor’s preference. Assignments put into the wrong drop slot will not be marked. Acknowledgements: be sure to acknowledge any help you get with a short paragraph at the end of the assignment ‘Warm up’ exercises: Not to be submitted, but we recommend you try these first. Answers are in the back of the text. From the text, exercises 7.5 # 1, 5, and 9. Part A (answer only): Submit your answers (not full solutions) using the template provided on the last page of this assignment, which you can print or hand-copy. Text exercises 7.5 # 2, 18, 30, and 7.8 # 2 (no need to submit answer to ‘why’). Part B (full solution): All solutions must be clearly stated and fully justified. 1-9. Evaluate the following integrals using an appropriate technique. If the integral is improper, evaluate it (if it converges) or explain why it diverges.

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Unformatted text preview: 1. Z x 2 sin xdx 2. Z arcsin(2 x ) dx 3. Z x 3 ( x-2) 2 dx 4. Z z 1 + z 4 dz 5. 2 Z 1 x + 1 x 3 + x dx 6. Z x x 4 + x 2 + 1 dx 7. √ 2 / 2 Z x 2 √ 1-x 2 dx 8. Z ∞ 1 e-3 x dx 9. Z 3 2 1 √ 3-x dx 10. An application from the text: 7.8 # 68. Comment: normally, we let k be a positive number, and write e-kt so that it’s clear that we have exponential decay. In this question, k is negative, so e kt is gives exponential decay (the minus sign is ‘built in’ to the k ). Just be careful and remember that k is negative . 11.* Planck’s Radiation Law involves the integral I = Z ∞ 1 dx x 5 ( e 1 /x-1) . Show that e t ≥ 1+ t for t ≥ 0, hence explain brieﬂy why the integral I must converge. Answers to Part A problems: Question Answer 7.5 # 2 7.5 # 18 7.5 # 30 7.8 # 2 Reminder: please submit your full solutions for part B problems only....
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