Chapter72004solutions

Chapter72004solutions - Chapter 7 Test 1 February 3 2004 No...

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Chapter 7 Test February 3, 2004 No Calculators Name 1. Find the area of the region bounded by the graphs of the equations y = 1 and y = sin 2 x from x = −π ccccccc 2 to x = π cccc 2 . π cccc 2 π cccc 4 π cccc 4 π cccc 2 x 0.5 1 y y = 1 y = sin 2 @ x D A = 2 0 π ccc 2 H 1 six 2 x L dx = 2 0 π ccc 2 i k j j 1 i k j j 1 cccc 2 1 cccc 2 cos 2 x y { z z y { z z dx = 2 0 π ccc 2 i k j j 1 cccc 2 + 1 cccc 2 cos 2 x y { z z dx = 2 A 1 cccc 2 x + 1 cccc 4 sin 2 x E 0 π ccc 2 = 2 AJ π cccc 4 + 0 N H 0 + 0 LE = π cccc 2 2. Find the volume of the solid generated by revolving the region bounded by x = 1 cccc 3 y, 2 y = x, and x = 2 about the x axis. V washers 0 2 AH 3 x L 2 i k j j 1 cccc 2 x y { z z 2 E dx 0 2 i k j j 9 x 2 1 cccc 4 x 2 y { z z dx = 35 cccccc 4 π 0 2 x 2 dx = 35 12 π @ x 3 D 0 2 = 35 12 π H 8 L = 70 π cccccccccc 3 3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations x =− è!!! y, y 3 = 2 x, and x = 0 about the y axis.
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V shells = 2 π 1 0 H x L H 2 x + 3 x 2 L dx = 2 π 1 0 H x 3 2 x 2 3 x L dx = 2 π A 1 cccc 4 x 4 2 cccc 3 x 3 3 cccc 2 x 2 E 1 0 = 2 π A 0 i k j j 1 cccc 4 + 2 cccc 3 3 cccc 2 y { z zE = 2 π i k j j 18 8 3 cccccccccccccccc ccccccccccc 12 y { z z = 7 π ccccccc 6 4. A solid has as its base the region in the xy plane determined by the graph of the ellipse, x 2 + 4 y
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Chapter72004solutions - Chapter 7 Test 1 February 3 2004 No...

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