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Math Help - Sum of points in an exponential equation

  1. #1
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    Sum of points in an exponential equation

    I'm not sure which sub-board this goes in, so I'm sorry if I chose wrong.

    How can you find the sum of all points of an exponential within a certain range? That is:

    f(x) = a * x ^ y

    I figure the result would be same as the area of the region underneath the curve, above the x-axis, and between the two points (start and end), as highlighted pink in the graph (not included due to errors uploading), but I'm not finding a formula for that either.
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  2. #2
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    It looks to me like you've posted in the correct subforum.

    I have a question: what is y in your f(x)?
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  3. #3
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    y is an arbitrary real number, and 'a' is a non-negative integer. Only non-negative results are significant. I think I wrote the function wrong. How's:

    f(a, x, y) = a * x ^ y
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  4. #4
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    So is x the only independent parameter you are varying? That is, do you just want to fix a and y, and find the area under the curve for some interval p < x < q?
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  5. #5
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    Yes, that's it! Sorry.

    EDIT: Now, I wish I spent more time learning proper notation.
    Last edited by qformat; May 6th 2011 at 04:03 AM.
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  6. #6
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    So that means you wish to compute

    \int_{p}^{q}a x^{y}\,dx=a\int_{p}^{q}x^{y}\,dx.

    You can use the power rule here:

    \int x^{n}\,dx=\frac{x^{n+1}}{n+1}

    to get the antiderivative, and then plug in your limits. What do you get?
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  7. #7
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    Hang on while I learn Calculus.
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  8. #8
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    Quote Originally Posted by qformat View Post
    Hang on while I learn Calculus.
    Oh. Well, in that case, let me just compute that for you. I get

    a\int_{p}^{q}x^{y}\,dx=\frac{a}{y+1}\left(q^{y}-p^{y}\right).

    This is a problem you would learn how to solve pretty early on in the second semester of calculus (so, after your review of functions, after limits, continuity, and differentiation).

    [EDIT]: See below for a correction.
    Last edited by Ackbeet; May 6th 2011 at 05:35 AM.
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  9. #9
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    Wow, I was getting something completely different. I want to go back to school. I better go through the rest of these online tutorials before my next problem. I feel like a primitive aborigine with the privilege of being graced by a modern caretaker. Thank you so much.
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  10. #10
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    Correction: it should be

    \frac{a}{y+1}(q^{y+1}-p^{y+1}).

    Try that out.
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