What is the volume of the solid produced by revolving #f(x)=tanx, x in [0,pi/4] #around the x-axis?

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Answer 1 · 2017-04-13T09:39:00

The volume is #=0.67u^3#

We need
#sin^2x+cos^2x=1#

Dividing by #cos^2x#

#tan^2x+1=sec^2x#

#tan^2x=sec^2x-1#

and

#intsec^2xdx=tanx#

A small volume is

#dV=piy^2dx#

So,

#V=piint_0^(pi/4)tan^2xdx#

#=piint_0^(pi/4)(sec^2x-1)dx#

#=pi[tanx-x]_0^(pi/4)#

#=pi(1-pi/4-0)#

#=0.67#