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  1. #1
    la vache fantôme phantomcow2's Avatar
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    Express integral as limit of sums

    I started calc 2 this week. We're reviewing Reimann sums. I need to express the following as a limit of sums, but not calculate the limit.

    Integral of (2x+cosx)dx from 1 to 3

    So here I would find delta x, which is equal to -2/n. xi is equal to -2i/n

    summation f(xi)(delta x)

    summation (2(-2i/n) + cos(-2i/n))(-2/n)

    summation (-8i/n^2) + (-2/n)cos(-2i/n)

    summation (-8i/n^2) + summation [(2/n)cos(-2i/n)]

    Okay now what? usually I'd factor out the -8/n^2 from the first term, and the (-2/n) from the second term, putting it in front of the summation (sigma). Then I'd use one of my formulas to substitute, such as n(n-1)/2. But I what formula exists for cos(-2i/n)? I can't factor anything out here. Am I already done?
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  2. #2
    phony collective progress x136's Avatar
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    Last edited by x136; 05-28-09 at 09:11 PM.

  3. #3
    Hey guyz? Guyz? Wait up!! Siu Blue Wind's Avatar
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  4. #4
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    lim_(n->+-infinity) cosh(2/n) = 1
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


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  5. #5
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


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  6. #6
    My name is Mike, not Cal
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    Quote Originally Posted by Tom Stormcrowe View Post
    integral_1^3(2 x+cos(x)) dx = 8-sin(1)+sin(3)~~7.29965...
    Did you check WolframAlpha, too?
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  7. #7
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Quote Originally Posted by cal_gundert05 View Post
    Did you check WolframAlpha, too?
    No, I worked it out first, and then confirmed it afterward with Wolfram.
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche

    "We can judge the heart of a man by his treatment of animals." - Immanuel Kant

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