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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Sunday, March 12, 2006

When test time comes, be ready

It doesn't matter what you do in before the test, what matters is what you do on your own time. This unit was fairly short, section 1 was net distance which is the integral of the velocity function and total distance traveled which is the absolute value of the velocity function then take the integral of that. Section 2 was volumes by slicing, which involves revolving the graph of a function around the x-axis. You can find the volume of that solid by finding the integral from (a,b) of the function A(x). A(x)=(pi)(x)², x represents the radius of the circle, which is the function value. If it is a washer then in place of x, subtract the smaller function from the larger function. In section 3 there was the shell method for solving a problem if a function was revolved around the y-axis. The volume of that solid can be found by taking the integral from (a,b) for 2(pi)*x*f(x). Section 4 was the average value over an interval. The average value of a function is represented by the integral from (a,b) integrate f(x) and multiply it by the constant (1/(b-a)). Section 5 was the hard part of the unit, WORK, and DENSITY. Work = (Force)*(Distance) and Density= mass/volume. The best way to attempt these problems is to break them up in pieces and figure out what each part of the equation is before attempting to find the final solution. For example, if you have a WORK problem, find the FORCE and then find the DISTANCE before combining them in an integral. The problems from this section of the textbook are the hardest we've faced thus far, so good luck.

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