Chapter72008solutions - Chapter 7 Test January 31, 2008 No...

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Chapter 7 Test January 31, 2008 No Calculators Name 1. Find the area of the region bounded by the graphs of the equations x = 8y, x =- 8, and x y 3 A = - 8 0 A - x 1 ÄÄÄ 3 - 1 ÄÄÄÄÄ 8 x E dx = A - 3 ÄÄÄÄÄÄÄÄ 4 x 4 ÄÄÄ 3 - 1 ÄÄÄÄÄÄÄ 16 x 2 D - 8 0 = 12 + 4 = 16 2. A solid has as its base the region in the xy - plane bounded by the graph of the equations 4 x 2 + y 2 = 16. Every cross section by a plane perpendicular to the x - axis is an equilateral triangle, with one side in the xy - plane. Find the volume of the solid. y "################ ##### 16 - 4 x 2 2 "############ 4 - x 2 so V = 2 0 2 è!!!! 3 ÄÄÄÄÄÄÄÄÄÄÄÄ 4 i k j j 4 "############ 4 - x 2 y { z z 2 dx = 8 "#### 3 0 2 H 4 - x 2 L dx = 8 3 A 4 x - x 3 ÄÄÄÄÄÄÄ 3 D 0 2 = 128 3 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄ 3 3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = sin x ÄÄÄÄÄ 2 and y = cos x ÄÄÄÄÄ 2 , on the interval A 0, p ÄÄÄÄÄ 2 E , about the x - axis. V washers =p 0 p ÄÄÄ 2 A cos 2 J x ÄÄÄÄÄ 2 N - sin 2 J x ÄÄÄÄÄ 2 NE dx 0 p ÄÄÄ 2 cosx dx A sinx D 0 p ÄÄÄ 2 4. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations
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This note was uploaded on 08/29/2010 for the course MATH 44323 taught by Professor Anderson during the Spring '09 term at University of California, Berkeley.

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Chapter72008solutions - Chapter 7 Test January 31, 2008 No...

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