Posted by **Christina** on Monday, May 28, 2012 at 9:02pm.

Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6

- Calculus -
**Reiny**, Monday, May 28, 2012 at 10:22pm
y=2 intersects xy=6 at (3,2)

So we are rotating the region bounded by

(3,2) to (6,2), then down to (6,1) and joining the curve back to (3,2)

Vol = π∫(6-x)^2 dy from y = 1 to 2

= π∫(36 - 12x + x^2) dy

=π∫(36 - 12(6/y) + 36/y^2) dy from 1 to 2

= π[ 36y - 72lny - 36/y ] from 1 to 2

= π( (72 - 72ln2 - 18) - (36 - 72ln1 - 36) )

= π(54 - 72ln2)

= 18π(3 - 4ln2) or appr 12.86

check my arithmetic

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