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Unformatted text preview: Page 1 Assignment 8 150 points total Section 16.2 Problem 10 : sin ? ???Â¡ Â¡ 3 = âˆ’ sin 3 + 3 . Problem 16 : two sides of the triangle have equations: ? = Â¡ âˆ’ 1 2 Â¢? ? = Â¡ âˆ’ 5 âˆ’ 2 ???Â¡ âˆ’ 1 2 Â£Â¡âˆ’ 5 Â¤ 1 2 Â£Â¡âˆ’ 1 Â¤ 3 1 Problem 22 : Â£? 2 + Â¡ 2 Â¤?Â¡?? 2 ? 3 = 14 3 ? 3 ?? 3 = Â¥ Â¦ 14 12 ? 4 Â§Â¨ 3 = 94.5 Problem 36 : as given, the region of integration is as shown in the below figure. Reversing the limits gives Â© 2 + ? 3 ???Â¡ 1 Âª Â¡ 1 = Â© 2 + ? 3 ?Â¡?? ? 2 1 = ? 2 Â© 2 + ? 3 ?? 1 = 2 9 Â« 3 Âª 3 âˆ’ 2 Âª 2 Â¬ Page 2 Section 16.3 Problem 4 : ?? Â¡ = sin Â¢ cos Â£Â¤ + ?Â¥ ???Â¤?Â¢ Â¦ Â¦ Â¦ = sin Â¢ [sin Â£Â¤ + Â¦Â¥ âˆ’ sin Â¤ ] ?Â¤?Â¢ Â¦ Â¦ = âˆ’ 2 2 sin Â¢ ?Â¢ Â¦ = âˆ’ 8 Problem 20 : A slice through Â¡ for a fixed value of Â¢ is a semicricle the boundary of which is Â¤ 2 = Â§ 2 âˆ’ Â¢ 2 âˆ’ ? 2 , for Â¤ â‰¥ , so the inner integral is Â£Â¢ , Â¤ , ?Â¥?Â¤ Â¨Â§ 2 âˆ’Â¢ 2 âˆ’?...
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 Fall '08
 FORTMANN
 Coordinate system, Polar coordinate system, Coordinate systems, Cylindrical coordinate system

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