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hw8-sol - Page 1 Assignment 8 150 points total Section 16.2...

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Unformatted text preview: Page 1 Assignment 8 150 points total Section 16.2 Problem 10 : sin ? ???¡ ¡ 3 = − sin 3 + 3 . Problem 16 : two sides of the triangle have equations: ? = ¡ − 1 2 ¢? ? = ¡ − 5 − 2 ???¡ − 1 2 £¡− 5 ¤ 1 2 £¡− 1 ¤ 3 1 Problem 22 : £? 2 + ¡ 2 ¤?¡?? 2 ? 3 = 14 3 ? 3 ?? 3 = ¥ ¦ 14 12 ? 4 §¨ 3 = 94.5 Problem 36 : as given, the region of integration is as shown in the below figure. Reversing the limits gives © 2 + ? 3 ???¡ 1 ª ¡ 1 = © 2 + ? 3 ?¡?? ? 2 1 = ? 2 © 2 + ? 3 ?? 1 = 2 9 « 3 ª 3 − 2 ª 2 ¬ Page 2 Section 16.3 Problem 4 : ?? ¡ = sin ¢ cos £¤ + ?¥ ???¤?¢ ¦ ¦ ¦ = sin ¢ [sin £¤ + ¦¥ − sin ¤ ] ?¤?¢ ¦ ¦ = − 2 2 sin ¢ ?¢ ¦ = − 8 Problem 20 : A slice through ¡ for a fixed value of ¢ is a semi-cricle the boundary of which is ¤ 2 = § 2 − ¢ 2 − ? 2 , for ¤ ≥ , so the inner integral is £¢ , ¤ , ?¥?¤ ¨§ 2 −¢ 2 −?...
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