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.

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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Willowbrook, IL

Use disk method.

Infinitesimally small volume of a disk is given by:

dV=πr(x)^{2}dx, where r(x) is the radius of the disk, dx is its thickness.

r(x)=y(x)=sec (x)

Thus,

V=π∫_{0}^{π/3}sec^{2}(x)dx=π(tan(π/3)-tan(0))=π√3

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