# How do you find the surface area of the solid obtained by rotating about the #x#-axis the region bounded by #9x=y^2+18# on the interval #2<=x<=6# ?

##### 1 Answer

Sep 20, 2014

The surface area can be found by

Let us look at some details.

By taking the derivative,

As x goes from 2 to 6, y goes from 0 to 6.

Since the surface area of revolution can be found by

we have

by substitution

As y goes from 0 to 6, u goes from 1 to 25/9.

by simplifying,