How do you find the volume of a solid that is enclosed by #y=1/x#, x=1, x=3, y=0 revolved about the y axis?
1 Answer
Explanation:
The shape that we are integrating should look something like a big top for a circus. We may have to split up the top and the bottom halves at
We can use an integration over
To find the area of a slice we look at points below
Below
The outer radius is constant at 3. There is an inner radius cut out from the
Above
The bound is a little more complicated above
In this region, the inner radius is still a constant (hence a
We can integrate this whole thing piecewise:
Therefore, the total volume is