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Chapter72005solutions

Chapter72005solutions - Chapter 7 Test 1 February 1 2005 y...

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Chapter 7 Test February 1, 2005 No Calculators Name 1. Find the area of the region bounded by the graphs of the equations y 2 = 4 + x and y 2 + x = 2. 4 3 2 1 1 2 x 2 1 1 2 y y 2 = 4 + x y 2 + x = 2 x = y 2 4, x = 2 y 2 y 2 4 = 2 y 2 2 y 2 = 6 y = ± è!!! 3 A = 2 0 è!!!! 3 @H 2 y 2 L H y 2 4 LD dy = 2 0 è!!!! 3 @ 6 2 y 2 D dy = 2 A 6 y 2 cccc 3 y 3 D 0 è!!!! 3 = 2 I 6 è!!! 3 2 è!!! 3 M = 8 è!!! 3 2. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations x = è!!!!!!!!!!!!!!!!! 25 y 2 and x = 3 about the y axis. V washers = 2 π 0 4 AI è!!!!!!!!!!!!!! 25 y 2 M 2 3 2 E dy = 2 π 0 4 @ 16 y 2 D dy = 2 π A 16 y 1 cccc 3 y 3 D 0 4 = 2 π i k j j 64 64 ccccccc 3 y { z z = 2 π i k j j 128 cccccccccc 3 y { z z = 256 π ccccccccccccc 3 3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = è!!!!!!!!!!!! x 2 , y = 1 and x = 6 about the x axis.
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V washers = π 3 6 JI è!!!!!!!!!! x 2 M 2 1 2 N dx = π 3 6 H x 2 1 L dx = π 3 6 H x 3 L dx = π A 1 cccc 2 x 2 3 x D 3 6 = π AH 18 18 L i k j j 9 cccc 2 9 y { z zE = 9 cccc 2 π 4. A solid has as its base the region in the xy
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