Monday, February 8, 2010

Ash's 25th Post Part II

I can finally post my blog and do my wiki because: YAY!! THE VIRUS IS GONE FROM MY COMPUTER!! (Trojan)
But along with that being gone, each time I click something the "Open With" box pops up!! *throws computer against the wall* Does anyone know how to fix this?

Fun Fact of the week:
I was watching The Lion King and in Scar's song "Be Prepared" he refers to math with these lyrics: "And injustice deliciously squared"
And there's the random math fact of the week!!

Okay, so, that out of the way, let's move on to important things.

AP Tests = not fun.
How is everyone else doing? are you improving at all? I found the last test to be pretty...I dunno, out there?
The Calculator potion killed me! (nevermind the fact that my calculator decided to be stupid and not work)
I want to try to explain something, but I don't want to explain it wrong and confuse myself and others.

I need help with remembering what to do when. Okay, let me change that.
I know what to do, I just can't do it. Does anyone else have this problem?
I'm getting stuck on large derivatives and integrating fractions. Can anyone give me an example problem of integrating fractions or tips? It's on every AP test and it kills me that I can't figure it out! -.-
Please and thank you!!

5 comments:

  1. One tip for Fractions is you can check to see if it is one of three things:

    1. ln integration- if the top is the derivative of the bottom, then you know your u is the bottom.

    2. Tan inverse- if you have a fraction and it has a + 1 on the bottom, then it is most likely tan inverse.

    3. If nothing else, then you most likely have to use substitution to get the integral you are looking for.

    Hope this helps!

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  2. So when you are trying to integrate a fraction, the first thing to check for if it is a natural log. If the top is the derivative of the bottom, then you know you will have a natural log.
    EXAMPLE: Integrate 2x/1+x^2
    The derivative of the bottom is 2x which is also the top; therefore it is a natural log integration. The answer is ln |1+x^2| + c

    EXAMPLE 2: Integrate cos x/ sin x
    The derivative of sin is cos so the answer is ln |sin x| + c

    Another common fraction integral problem is tan inverse.
    Tan inverse integration is recognized by the +1 in the denominator. To do tan inverse integration, pull the number out in front and then its the tan inverse of the square root + c.
    EXAMPLE 3: Integrate 7/x^2 + 1. The +1 lets you know it is tan inverse. From there, pull 7 to the front then take the square root of x^2.
    7 tan inverse (x) +c

    These are the two main fraction integrals I can think of.

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  3. For integrating fractions, there are a few things you should keep your eye out for.

    tan inverse-if there is a fraction and on the bottom there is a + 1, it usually is tan inverse

    ln integration- when the top is the derivative of the bottom, make the bottom equation your u.

    And when all else fails, substitution is used.

    Good luck :)

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  4. When integrating fractions just make sure you first look to see if it is a natural log (the derivative of the bottom is the top). If it is not, try to break up anything you can to make it easier.

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  5. Also keep in mind that tan(x) is sin(x)/cos(x) they try to trick you by just asking for the integral of tan(x) or cot(x)

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