How do you find the volume of the region bounded b the line #y = x-2#, the x-axis, #x=2#, and #x=4# is revolved about the line #x = -1#?

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Answer 1 · 2015-10-18T22:18:04

#V=(52pi)/3#

#V=pi int_(y_1)^(y_2) (R^2-r^2)dy#

#y=x-2, x=2 => y_1=2-2=0#
#y=x-2, x=4 => y_2=4-2=2#

#x=4 => R=4-(-1)=5#
#y=x-2 => x=y+2 => r=y+2-(-1)=y+3#

#V=pi int_(0)^(2) (5^2-(y+3)^2)dy = pi int_(0)^(2) (25-y^2-6y-9)dy#

#V=pi (16y-3y^2-y^3/3) |_0^2 = pi (32-12-8/3)#

#V=(52pi)/3#