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Unformatted text preview: 1. Z x 2 sin xdx 2. Z arcsin(2 x ) dx 3. Z x 3 ( x2) 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 √ 1x 2 dx 8. Z ∞ 1 e3 x dx 9. Z 3 2 1 √ 3x dx 10. An application from the text: 7.8 # 68. Comment: normally, we let k be a positive number, and write ekt 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 /x1) . 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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 Spring '10
 Zuberman
 Math, Derivative, Radioactive Decay, dx

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