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Quick Notes
Area and Volume is always an FRQ on the AB exam, and there will be either a standard Area and Volume or Polar FRQ on the BC exam. This is frequently assessed on MCQs as well.
Usually you will be given a region in the plan and asked to determine its area as well as the volume of various solids related to the region.
You will need to find any points of intersection between graphs. If this is on a calculator active question, remember to store those values in order to avoid roundoff error.
Know when to set up your integral with respect to x (dx) or y (dy).
Remember that an integral, by definition, gives the area bound by a graph and the axis.
For area, you should also be prepared to find the area bound by two curves. Remember, top-bottom or right-left.
Remember that for volume, you are simply adding up the areas of all of the cross-sections, whether they are geometric shapes, discs, or washers.
For solids of revolution, don't forget to subtract the axis of rotation.
Occasionally, they will ask you to write, and possibly solve, an integral equation to find the line that divides a region in half.
On the BC exam, you may also see questions about arc length and polar area.
~ Related CED Units ~ 8
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