https://youtu.be/uGnusctB32o

In this video I go over the same example 3 on surface area which I covered in my last video but this time solve it by writing the integral in terms of x, solution 2, as opposed to solution 1 which was in terms of y. In this particular example writing the integral in terms of y skips the need to use the initial substitution for integrals technique which I covered in my last video. But the rest of the solution is the same as that in my last video, which is why I skipped the full derivation of this integral, so make sure to watch my last video as well!

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- YouTube: [https://youtu.be/uGnusctB32o](https://youtu.be/uGnusctB32o)

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# Applications of Integrals: Area of a Surface of Revolution: Example 3: Solution 2: x = ln(y)

Find the area of the surface generated by rotating the curve y = e<sup>x</sup>, 0 ≤ x ≤ 1, about the x-axis.

![](https://cdn.steemitimages.com/DQmYzvnFKmYkt42dHFSqT6TxBsBSAYWSBYCYwMW3iV3V5fA/image.png)

![](https://cdn.steemitimages.com/DQmeZ9Vxby1BjP2mAFS2Uj6iBFUrACrae4EwBE3DDGENfu7/image.png)

![](https://cdn.steemitimages.com/DQmVfysfx8KNsFZda5tvBDih37nSQAtgFmUMGRLKRRKGoCH/image.png)

![](https://cdn.steemitimages.com/DQmPYn7wUtpzerDh9PWQomLKUASkELmgSWmaJPDS3DvMqUj/image.png)