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Solids of revolution - disc method

12 videos
1 skill
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.

Disk method around x-axis

VIDEO 9:01 minutes
Finding the solid of revolution (constructed by revolving around the x-axis) using the disc method.

Generalizing disc method around x-axis

VIDEO 2:35 minutes
Generalizing what we did in the last video for f(x) to get the "formula" for using the disc method around the x-axis

Disc method around y-axis

VIDEO 7:33 minutes
Finding the volume of a figure that is rotated around the y-axis using the disc method

Disc method (washer method) for rotation around x-axis

VIDEO 9:07 minutes
Finding the volume of a solid of revolution that is defined between two functions

Generalizing the washer method

VIDEO 8:31 minutes
Looking at the example from the last video in a more generalized way

Disc method rotation around horizontal line

VIDEO 9:54 minutes
Solid of revolution constructing by rotating around line that is not an axis

Washer method rotating around non-axis

VIDEO 6:38 minutes
Washer method when rotating around a horizontal line that is not the x-axis

Part 2 of washer for non axis rotation

VIDEO 8:14 minutes
Doing some hairy algebra and arithmetic to evaluate the definite integral from the last video

Disc method rotating around vertical line

VIDEO 4:51 minutes
Volume of solid created by rotating around vertical line that is not the y-axis using the disc method.

Calculating integral disc method around vertical line

VIDEO 5:39 minutes
Let's calculate the integral from the last video.

Washer or ring method for vertical line rotation

VIDEO 7:50 minutes
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 for washer method around vertical line

VIDEO 5:35 minutes
Evaluating integral set up in the last video using washer method.