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Find the volume?

Find the volume of the solid generated by rotating about the x-axis the region enclosed by the curve y=sec x and the lines x=0, y=0, and x=pi/3. 
 
Answer: pi*sqrt(3)
 
Please show all your work. Thanks.
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1 Answer

Use disk method.
 
Infinitesimally small volume of a disk is given by:
dV=πr(x)2dx, where r(x) is the radius of the disk, dx is its thickness. 
r(x)=y(x)=sec (x)
 
Thus,
V=π∫0π/3sec2(x)dx=π(tan(π/3)-tan(0))=π√3