# Question #75ad4

##### 1 Answer

**positive** X-axis is a boundary

#### Explanation:

We could do this with a memorized formula (skip to the end for the general formula), but here it is in a somewhat detailed form:

We are interested in the area bounded by

and the X-axis (where

(Note that

If we start by considering the

Then if we consider a thin disk with a thickness of

We can (hopefully) see that provided **sum** of all such disk volumes will be close to the volume of the entire rotated function.

In fact, it would be reasonable to claim that the volume of the rotated image of

[Take a moment to consider this.]

This is, of course, just an expansion of the normal notation:

Expanding

and then taking the indefinite integral:

We have the required volume:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

...and here is the promised general formula for a function

where

If you followed through with the example, the reason for this general formula should be clear.