# How do you find the volume of the solid formed by rotating the region enclosed by ?

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about the x-axis.

about the x-axis.

##### 3 Answers

#### Explanation:

We'll use a method call the disk method to do this.

Take a look at the above picture. Pretend it's an infinitely small cylindrical disk, with radius

We know volume of a cylinder is given by:

And we know that the radius of each cylinder is the value of

Integrating both sides to find total volume, for

But

Expanding the

And using the sum rule:

Finally, evaluating these one by one:

Awesome Ken...

Here is a Maple rendering of the rotation!

By the way, you have the coolest name in the world.

0.9117

#### Explanation: