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Solids of revolution - shell method
You want to rotate a function around a vertical line, but do all your integrating in terms of x and f(x), then the shell method is your new friend. It is similarly fantastic when you want to rotate around a horizontal line but integrate in terms of y.
Introducing the shell method for rotation around a vertical line.
Evaluating the definite integral set up using the shell method
Find the volume of a solid of revolution by rotating around the x-axis using the shell method
Using the shell method to rotate around a vertical line.
Evaluating integral set up with shell method for two functions.
Stepping it up a notch, our solid is now defined in terms of two separate functions.
Volumes of solids of revolution, shell method