What is the volume obtained by rotating the region enclosed by #y=11-x#, #y=3x+7#, and #x=0# about the y-axis?

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Answer 1 · 2016-03-27T01:36:42

#V= V_1-V_2=11,525pi/27#
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Given: #y=11-x#, #y=3x+7#, and #x=0#
Required: The volume obtained by rotating about the y-axis
Solution strategy: looking at the figure we see that

#V= 2pi [int_(1)^11x(11-x)dx- int_(-2 1/3)^1x(3x+7)dx]#

#V_1 = 2pi [(11/2x^2-x^3/3)_1^11]#
#V_2 = 2pi [(x^3+7x^2/2)_(-2 1/3)^1]#
#V= V_1-V_2=11,525pi/27#