Disk-Washer Guidelines

# Disk-Washer Guidelines - (b If you are rotating about...

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Solving Solids of Revolution using the Disk/Washer Method 1. Draw a picture of the area you are rotating. You may need to ﬁnd the intersection points of two curves. 2. Draw a picture of the volume 3. Determine disk or washer (i.e. do you have a big ”R” and a little ”r”, or just a big ”R”) 4. Draw lines from the axis of rotation to the farthest and closest curve, representing R and r, respectively. (a) If you are rotating about something parallel to the y-axis your lines will be perpendicular to the y-axis (parallel to the x-axis). i.e. You’ll have a “dy” (b) If you are rotating about something parallel to the x-axis your lines will be perpendicular to the x-axis (parallel to the y-axis). i.e. You’ll have a “dx” 5. Determine R and r if necessary (a) If you are rotating about something parallel to the y-axis R and r need to be in terms of y
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Unformatted text preview: (b) If you are rotating about something parallel to the x-axis R and r need to be in terms of x 6. Determine your limits of integration. (a) If you are rotating about something parallel to the y-axis your limits will be y-coordinates. (b) If you are rotating about something parallel to the x-axis your limits will be x-coordinates. 7. If you have a disk use (a) b R a πR 2 dy if you are rotating about something parallel to the y-axis. (b) b R a πR 2 dx if you are rotating about something parallel to the x-axis 8. If you have a washer (a) b R a π [ R 2-r 2 ] dy if you are rotating about something parallel to the y-axis. (b) b R a π [ R 2-r 2 ] dx if you are rotating about something parallel to the x-axis...
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