Question

Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.

y = sqrt(x)
y = 0
x = 6

a) the x-axis
b) the y-axis
c) the line x=6
d) the line x=9

Answer 1

I'll start you off:


a) Use the method of rings/washers, \[r = \sqrt{x}\] and integrate from x=0 to x=6
b) Use the method of cylindrical shells. \[h = \sqrt{x}\] and integrate from x=0 to x=6
c) Same as b except think about where you're rotating, how will your radius change?
d) Once you've done c, you can do this
For more information see: http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx

Answer 2

Its x^(1/2) in the picture not x^2

Answer 3

So for a) would it be \[\int\limits_{0}^{6}x ^{1/2} dx\]? If so, how would b) be any different? I still dont understand C and D