So just to clarify the procedure for 1 (non 3U algebra method):
- Interpret from the information given that the region occurs when y >= 1 for the original equation
- Express the original equation in terms of x to find x <= 3
- Test a point on either side of the asymptote (x=2) with the original equation considering what's been obtained
- Shade the region
For 2 I tried integration initially but got the wrong answer. Don't think we covered volumes generated by an area between two intersecting functions. Are any of these on the right track? Should I be trying to split up the volumes and subtracting/adding them with separate integrations or does it work like the area between two intersecting functions?
(Image removed from quote.)
Testing is up to you and perfectly safe. I prefer using my intuition or doing it in my head but there's nothing wrong with testing if you know what you're doing.
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If you were rotating about the x-axis, you'd have a volume between two curves similar to the first one.
But you're rotating about the
y-axis. If you treated this is an area question, you would have a compound region and be adding the area integrals. Hence, you should be adding the volume integrals here as in equation 3.
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