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Math Help - Calculus Integrals

  1. #1
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    Calculus Integrals

    I have a final exam in an hour, I get understand everything but integrals. I don't have a bloody clue.

    A sample question is;

    Find the following integral;

    S (x^3 + 5x - 8)/(9x^5) d/dx

    I'm just completely lost. I must have missed the class(es) when we went over this, nothing in my notes, and I can't find anything in my textbook.

    I know an hour is a little short to learn this, but if someone could go over the general idea for me, I'm hoping I can steal a mark or two on those questions.
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  2. #2
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    What in the world is the "S"? I'm assuming you're trying to do an integral sign?

    So you want to find the integral of (x^3 + 5*x - 8)/(9*x^5)dx

    Do you agree we can expand the above to:

    1/(9*x^2) + 5/(9*x^4) - 8/(9*x^5)

    Then:

    Take the integral of each of the terms.

    Thus,

    -1/(9*x) + [-5/(27*x^3)] + [2/(9*x^4)] + C, where C is some constant.
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  3. #3
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    Yeah, its supposed to be that extended S integral sign thingy.

    But I think I'm screwed.

    I sorta get how you expanded it, but I don't know where the variable X went. And I don't even know what taking the integral means.

    Oh well, hopefully I'll do well in the other sections to make up for it.
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  4. #4
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    Quote Originally Posted by Sucker Punch View Post
    And I don't even know what taking the integral means.
    It means finding the "anti-derivative".
    That is a function whose derivative is equal to the function.

    For example,
    \int 2x dx=x^2
    Because,
    (x^2)'=2x

    In fact,
    \int 2xdx = x^2+1
    Because the constant term vanishes when you take the derivative.

    Thus, all anti-derivates must be,
    \int 2xdx=x^2+C
    Where C is any konstant function.
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