SOLUTION: Having trouble figuring this out- I know what to do but not sure how to format with the sqrt 1+x. Here is the question Find the volume generated by revolving about the x-axis t

Question 203895: Having trouble figuring this out- I know what to do but not sure how to format with the sqrt 1+x.
Here is the question
Find the volume generated by revolving about the x-axis the regions bounded by the following graphs:
y= sqrt 1+x
x= 2
x= 9
thanks

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I presume you are in a Calculus class. This problem is easier if we use the disc (or cylinder) method of finding the volume of revolution. (Look this up so youcan follow along because I will unable to provide sufficiently clear explanations and/or diagrams to make this self-explanatory.

Below is a graph of y = sqrt(x+1):

The disk method uses the volume of an infinitely thin cylinder (disk). (Picture this disk with the x-axis through the center. Now picture a "stack" of these disks, all centered on the x-axis running from x=2 to x = 9.) To find the volume of all these disks, we sum volumes of each disk over an interval.

The radius of each disk will be the distance from the x-axis (the axis of revolution) to the graph of y = sqrt(x+1). The height of the disk will be "dx". The volume of a cylinder is: . Replacing "r" with sqrt(x+1) and "h" with "dx" we get, for the volume of one disk:

The volume of all the disks, from x=2 to x=9, will be the following integral:
evaluated from 2 to 9:

I hope this was clear.

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