Find the volume?

Question

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.

Answer 1

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∫₀^π/3sec²(x)dx=π(tan(π/3)-tan(0))=π√3