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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.

Monday, February 13, 2006

Life's not easy

Never in a million times will I ever find ANTIDIFFERENTIATING easy. So to make the long story short, here's what I prepared for, to "somehow" pass the test. It's practically a list of formulae and other important notes for me to remember.
The INVERSE CHAIN RULE:
$\displaystyle \int F'(g(x))\cdot g'(x)\, dx=F(g(x))+C
$
The method of SUBSTITUTION:
  1. SUBSTITUTE by choosing u = g (x) and write du = g' (x) dx = (du / dx) = dx. Then subsitute both u and du to the original integral producing a new integral in the form of f(u).
  2. ANTIDIFFERENTIATE in terms of u. F ' (u) = f (u)
  3. RESUBSTITUTE g(x) to obtain the antiderivative in terms of x.

The method of INTEGRATION BY PARTS:

\[ 
\int f(x)g^\prime(x)~dx = f(x)g(x) - \int f^\prime(x)g(x)~dx 
 \]
* L I A T E *
Antiderivatives of the inverse of Trigonometric functions:

d/(dx)sin^(-1)x=1/(sqrt(1-x^2))
d/(dx)cos^(-1)x=-1/(sqrt(1-x^2))
d/(dx)tan^(-1)x=

1/(1+x^2)

And the NUMERICAL INTEGRATION

  • the MIDPOINT RULE
  • the TRAPEZOID RULE
  • and the SIMPSON SUM (where twice the value of the MIDPOINT is added to the TRAPEZOID value all over 3)



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3 Comments:

  • At 10:38 PM CST, Blogger Mr. Kuropatwa said…

    You're right Ara, antidifferentiating isn't easy -- it's one of the most difficult things we learn in calculus.

    But I've got to tell you, this is an impressive list of material you've put together to study from! I wonder, If you had posted it several days before the test, and some of your classmates did something similar, and you all started talking it over, learning from each other, then maybe I could join the conversation, together we could all fill in the holes in each other's knowledge, so that the day the test rolled around everyone might feel a lot more confident and do a lot better. (Whew! Finally, a period. LOOK! Another one. And another one. And ... OK ... I'll stop now.)

    What do you think? Is this something worth trying for our next unit of study?

     
  • At 7:22 PM CST, Blogger ara said…

    yeah... I guess you're right Mr. K. I should've posted that several days before the test. I could've had a better grade. Ohhh.. I've got to stop this cramming thingy before my mark gets out of hand. I don't know, maybe I just got used to doing tasks on the last minute. I mean, it has become a habit now. this is a serious problem Mr. K. YOU'VE GOT TO HELP ME!!! (choking!!!)

     
  • At 10:38 PM CST, Blogger Mr. Kuropatwa said…

    Sure Ara, but it's really the sort of thing that you have to do for yourself. I've got an idea though ...

    If you really think my suggestion in my previous comment is a good one lets see of we can, as a class, try to actually do it, 3 days before each test. For my part, I will try to remind everyone 4 days before each test so you can all post your study notes on the blog at least 3 days before the test -- from there it's really up to you guys to carry the ball.

    Now let's say, Ara, that only you really do this. OK, I'll bet dollars to donuts that if you wrote a post like this one 3 days before the test the rest of the class would join the conversation by commenting, posting in the chatbox and/or posting their own study notes.

    We've got a really great bunch of people in our class but what we most need now is a leader. ;-)

     

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