Find the volume bounded by f(x) = x^(2), g(x)= (1)/(x), and the line y = 3 by shells and disk method. The answers should be the same.

Question

I figured out that the bounds are either 1 to sqrt of 3 or 1 to 3. I am not sure. Any help would be appreicated. Thank you!

Answer 1

You did not mention whether you are calculating the volume if the region is rotated about the x axis or about the y axis.

In order to use the disk method, you will want to do everything in terms of y.

The bounds in the y direction are y=1 and y = 3.

The graphs of y = x^2 and y = 1/x intersect at the point (1,1).

If you are rotating the region about the x axis, it is more complicated. For the region in the bound between x = 1/3 and x = 1, the outer function is y = 3 while the inner is y = 1/x. For the region in the bound between x = 1 and x = sqrt(3), the outer function is y = 3 and the inner is y = x^2