Find the volume of the solid of revolution obtained when the region undr the graph of f(x)= (1/x)sec(1/x), from x=3/pi to x=4/pi, is rotated about the x-axis. Give your answers to 2 decimal places.

Lets see... When you have an integrable function , then the volume of the solid obtained by rotation about the x-axis is given by

(1)

In this case, you will need to find the value of

There are math packages than can save you the bother, but I guess they ask of you, to calculate by numerical integration. If this is the case, search your textbook for the appropriate method, or ask again if I talk crap.

Note: (1) holds true. (BO-RING... )

Consider a partition of [a,b], and intermediate points . In revolving the function, we obtain n-1 elementary volumes of cylinders, with height , radious and -therefore- volume . Adding up, we get the Riemmanian sum

as , due to integrability.