What is the volume of the solid produced by revolving #f(x)=sec, x in [pi/8,pi/3] #around the x-axis?

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Answer 1 · 2016-05-17T09:10:43

Volume #V=4.140107808" "#cubic units

Given equation #y=sec x# and #x# is from #pi/8# to #pi/3#.

Differential volume #dv=pi*r^2*dh# for circular solid disk

In terms of our variable

#dv=pi*f(x)^2*dx#

Volume #V#

#V=int dv=int_(pi/8)^(pi/3) pi*sec^2 x*dx#

#V=pi*[tan x]_(pi/8)^(pi/3)#

#V=pi*(tan pi/8-tan pi/3#)#

#V=4.140107808" "#cubic units

God bless....I hope the explanation is useful.