Section 2.3
The “Shell Method”
A. Vaughn Winchell, Howard Community College
Sometimes the disk/washer method is hard to
use.
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Source: Briggs, W. L., Cochran, L., Gillett, B.,
& Schulz, E. P. (2015). Calculus: Early
Transcendentals. Boston: Pearson.
A. Vaughn Winchell, Howard Community College
Here’s how the Shell Method works.
Source: Briggs, W. L., Cochran, L., Gillett, B., & Schulz, E. P. (2015). Calculus: Early
Transcendentals. Boston: Pearson.
A. Vaughn Winchell, Howard Community College
We divide the region R into subintervals along
the x-axis.
Source: Briggs, W. L., Cochran, L., Gillett, B., & Schulz, E. P. (2015). Calculus: Early
Transcendentals. Boston: Pearson.
A. Vaughn Winchell, Howard Community College
Now, what would we find if we took one of those “shells” and
“unwrapped” it, the way you can unwrap the label of a soup
can?
Source: Briggs, W. L., Cochran, L., Gillett,
B., & Schulz, E. P. (2015). Calculus:
Early Transcendentals. Boston: Pearson.
A. Vaughn Winchell, Howard Community College
Unwrapping the “soup label.”
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A. Vaughn Winchell, Howard Community College
Adding up all those soup labels.
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A. Vaughn Winchell, Howard Community College
What if the bottom of the region isn’t the
x-axis?
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A. Vaughn Winchell, Howard Community College
An example of the shell method.
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A. Vaughn Winchell, Howard Community College
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A. Vaughn Winchell, Howard Community College
A further complication: what if the axis of
revolution is a line that isn’t the x- or y-axis?
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A. Vaughn Winchell, Howard Community College
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A. Vaughn Winchell, Howard Community College
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A. Vaughn Winchell, Howard Community College
Trying to keep it all straight! (Slide 1 of 3,
for visual learners)
Source: Briggs, W. L., Cochran, L., Gillett, B., & Schulz, E. P. (2015). Calculus: Early Transcendentals.
Boston: Pearson.
A. Vaughn Winchell, Howard Community College
Trying to keep it all straight! (Slide 2 of 3)
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A. Vaughn Winchell, Howard Community College
Trying to keep it all straight! (Slide 3of 3)
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A. Vaughn Winchell, Howard Community College