https://youtu.be/I6EDCqayvBY

In this video I go over another example on finding the volume of a shape formed by rotating a function about the x-axis. In this example I solve the volume of the shaper formed by rotating the function y = x<sup>1/2</sup> or y = sqrt(x) about the x-axis from x = 0 to 1.

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# Integrals and Volumes: Example 2

![Integrals and Volumes Example 2.jpeg](https://cdn.steemitimages.com/DQmdsxvXMUhbQTcDP44tR4qzZGGE8Y74d9odfbnv9XKgSe2/Integrals%20and%20Volumes%20Example%202.jpeg)

**Example:**

Find the volume of the solid obtained by  rotating about the x-axis the region under the curve y =x<sup>1/</sup>2 from 0 to 1. Illustrate the definition of volume by sketching a typical approximating cylinder.

**Solution:**

![](https://cdn.steemitimages.com/DQmToc9xFsBEfLU9BS5ZV8a47XJFFfN8wdDRLNVVXGQvjde/image.png)

Did we get a reasonable answer?? We can double check by considering the function y = 1 instead.

![](https://cdn.steemitimages.com/DQmQzPeBrKN7hQcbAVSYdNPm8WhtzzUNTKdjAVc9AC2yM5W/image.png)

Thus in our example the volume is computed as half this cylinder's volume, which seems about right.