AP Calculus

We spent the first part of class talking about the applications of derivatives. It breaks into two different concepts 1. The area under a curve or area between curves and 2. Average volume. We had already gone over the area under curves, but we covered between curves.

With the two functions, find the points of intersection to find the height of the segment that connects them. You then take the definite integral of the upper curve minus the lower. If they switch, you add the second part on to the first still using upper minus lower. Note: if one of your equations is negative, they will just add. E.g. 2- -4=6.

We then worked on the average value.

If given a velocity curve finding the definite integral of v(t)dt from points 1 to 5 gives displacement, and the displacement divided by the time interval gives average velocity. The average is ALWAYS the average value of f(x), or in terms of velocity, average turns into the average velocity.

We then spent a little bit of time reviewing the homework with led to the definite integral of 1/x is the same as the natural log.

We did problem 63 exactly.

We also noted that calc only deals with real numbers.

The homework is the Riemann Sum sheet and the 18 problems in the packet that are due Friday.

This entry was posted on Tuesday, March 17th, 2009 at 6:55 pm and is filed under Class Notes and Assignments 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.