AP Calculus

Today in class we reviewed some of the material and ideas we discussed before vacation. We went over a set of problems from the website entitled “Area Between a Curve and the x-axis” on Mrs. Evrard’s website. Here are some key concepts from this activity to remember:
1.

2. If a < b the definite integral will be negative because the dx is positive and the f(x) is negative
a. This has to do with the fact that

b. For example there is a difference between these two functions in problem number 5 on the website activity

f(x) is negative and dx is negative therefore their product is positive (see problem number five on the website for the exact question asked and to see the graph of this function).

f(x) is negative and dx is positive therefore their product is negative (once again see problem number 5 for the question and graph).
3. You may have to break a given definite integral into parts in order to solve the expression using the calculus method
a. For example in problem number 3 with the expression

These have to be broken up because there are different functions represented in the piecewise function.

Today we also reviewed the multiple-choice quiz we took a few weeks ago. We will have a quiz on Thursday over the same material as that antiderivative quiz. For more practice with these types of problem see pages 224 and 193 in the text. The most important thing to remember when solving these types of problems is to simplify the expression as best as you can to make finding the antiderivative easier.

The homework for next class is to study for the quiz next class and do problems 5, 8, 12, and 15 from the packet that starts on page 237 that was given to us in class.

This entry was posted on Tuesday, February 26th, 2008 at 2:03 pm and is filed under Class Notes and Assignments, Passed Entries and You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.