- Make sure your calculator is in radian mode
- Sketch two-dimensional graphs of regions carefully on your test (you can use the calculator to graph functions) - use your sketch to label radii and/heights
- For some of the regions, you will need to solve for intersection points (2nd-Calc-5 on calculator); store these as constants in your calculator for easy recall and accuracy
- Don't forget pi in front of the integral for disc & washer methods and 2pi in front of the integral for shell method and surface area
- For washer method, be sure your integrand is (R^2 - r^2) and not (R-r)^2
- When finding volume with semi-circle cross sections, be sure to square the radius (this will be 1/2 of the side length you would use for square cross sections) and not the diameter (a common error)
- Remember to use the amount a spring has been stretched or compressed for the integral limits (and not the actual length of the spring)
- Round all numerical answers to three digits after the decimal point
The mean scores on the tests I have given on this chapter in the past few years have been between 90 and 92 with about 60 to 70 with an A. There will not be a curve on this test. I would be thrilled with everyone earning a high score, but let's make sure that no one earns < 70!
I've had students ask if I will implement a bonus if everyone is present tomorrow for the test ... let's have no absences and you'll find out!
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