Calculus: Comparison of the the Disk\/Washer and the Shell Methods Sandra Peterson, Learning Lab - Calculus Comparison of the the Disk\/Washer and the

Calculus: Comparison of the the Disk/Washer and the Shell Methods Sandra Peterson, Learning Lab

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Calculus: Comparison of the the Disk/Washer and the Shell Methods Sandra Peterson, Learning Lab Prerequisite Material: It is assumed that the reader is familiar with the following: Method Axis of Revolution Formula Notes about the Representative Rectangle Disk Method x-axis ( ) [ ] dx x f V b a = 2 ( ) x f is the length dx is the width y-axis ( ) [ ] dy y g V d c = 2 ( ) y g is the length dy is the width Washer Method x-axis ( ) [ ] ( ) [ ] ( ) dx x g x f V b a = 2 2 π ( ) x f is the top curve ( ) x g is the bottom curve dx is the width y-axis ( ) [ ] ( ) [ ] ( ) dy y g y f V d c = 2 2 π ( ) y f is the right curve ( ) y g is the left curve dy is the width Shell Method x-axis ( ) [ ] dy y g y V d c = π 2 y is the distance to the axis of revolution ( ) y g is the length dy is the width y-axis ( ) [ ] dx x f x V b a = π 2 x is the distance to the axis of revolution ( ) x f is the length dx is the width It is important to note that the representative rectangle in the Disk and the Washer Methods are always going to be perpendicular to the axis of revolution. With the Shell Method, the representative rectangle will always be parallel to the axis of revolution.

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