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Solids of revolution - disc method
You know how to use definite integrals to find areas under curves. We now take that idea for "spin" by thinking about the volumes of things created when you rotate functions around various lines.
This tutorial focuses on the "disc method" and the "washer method" for these types of problems.
Finding the solid of revolution (constructed by revolving around the x-axis) using the disc method.
Generalizing what we did in the last video for f(x) to get the "formula" for using the disc method around the x-axis
Finding the volume of a figure that is rotated around the y-axis using the disc method
Finding the volume of a solid of revolution that is defined between two functions
Looking at the example from the last video in a more generalized way
Solid of revolution constructing by rotating around line that is not an axis
Washer method when rotating around a horizontal line that is not the x-axis
Doing some hairy algebra and arithmetic to evaluate the definite integral from the last video
Volume of solid created by rotating around vertical line that is not the y-axis using the disc method.
Let's calculate the integral from the last video.
Setting up the definite integral for the volume of a solid of revolution around a vertical line using the "washer" or "ring" method.
Evaluating integral set up in the last video using washer method.