STEM Lessons for College Students

Volume about y = x

In this video, I calculate the volume of a solid of revolution, but this time where the solid is rotated about the line y = x instead of the usual horizontal or vertical lines in calculus! This requires us to rotate the plane by 45 degrees, which in turn requires a sprinkle of linear algebra. This again should show how powerful linear algebra is, it allows us to solve impossible calculus problems. Enjoy!

Note: My apologies that I didn’t calculate the integral at the end. Here’s how to calculate the integral: https://youtu.be/M-s00EgQ7dA The answer is pi/120

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