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Math Help - calculus summations

  1. #1
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    Angry calculus summations

    i missed class today because of a field trip, so i'm completely lost. if anyone could help explain how to do these that would be greatly appreciated! thank you. I don't need an answer, i just need to know how to set up summations

    1.) use the Left Endpoint Rectangle Approximation Method to approximate the area
    integral from 0 to 2 of x^3 dx
    and the Right Endpoint Rectangle Approximation Method for the same problem

    2.) integral from 1 to 4 of (x)^(1/2) dx using the trapezoidal rule, left endpt RAM, right endpt RAM, midpt RAM

    3.) integral from 0 to pi of cosx dx
    trapezoidal rule, left endpt RAM, right endpt RAM, and midpt RAM
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  2. #2
    Member billa's Avatar
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    Maybe this will help, someone will explain it better soon no doubt

    When doing the LRAM summation you choose a width of x for your rectangles (like 1/2) and then you cut up the graph into sections. The find the area of each rectangle by multiplying base times height. With the Left RAM you choose the y value at the top left corner of each rectangle. So the sum is

    width*height (height is the y value at the left top corner)
    width is always whatever you chose at the beginning like 1/2 for example

    1/2 * 0 + 1/2 * (1/2)^2 + 1/2 * (1)^2 + 1/2 * (3/2)^2

    Hopefully that helps a little, I am not sure exactly what you meant
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  3. #3
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    There are formulae for setting these up:

    left rectangle rule: <br />
\frac{b-a}{n}\sum_{i=0}^{n-1}f(a+i\frac{b-a}{n})

    right rectangle rule <br />
\frac{b-a}{n}\sum_{i=1}^{n}f(a+i\frac{b-a}{n})

    trapezoidal rule
    <br />
\frac{b-a}{n}\sum_{i=1}^{n-1}f(a+i\frac{b-a}{n})+\frac12 f(a)+\frac12 f(b)

    midpoint rule
    \frac{b-a}{n}\sum_{i=0}^{n-1}f(a+\frac{b-a}{2n}+i\frac{b-a}{n})

    I suggest you look at the google image search for midpoint rule, trapezoid rule, left rectangle approx and right rectangle approx to get a better idea of what these are doing.
    Last edited by badgerigar; December 16th 2008 at 02:29 PM. Reason: all of the formulae were wrong
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  4. #4
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    Probably meant for this thread:
    thank you! im still confused on summations though.
    f(x)= 1/(x+1) from [0,1] and n=2
    how do i set up the summation for LRAM, RRAM, MRAM, and the trapezoidal method?
    EDIT: Sorry all of those formulas are wrong. I will fix them now
    Edit: fixed now. No wonder you were having trouble
    Sorry, I forgot to say what all of the letters stood for.
    (a,b) is the x-interval you are finding the area above.
    n is the number of subintervals you divide that interval into.

    So for the left rectangle rule you should get
    \frac{b-a}{n}\sum_{i=0}^{n-1}f(a+i\frac{b-a}{n})
    =\frac{1-0}{2}\sum_{i=0}^{2-1}f(0+i\frac{1-0}{2})
    =\frac{1}{2}\sum_{i=0}^{1}f(i\frac{1}{2})

    The other rules are similar
    Last edited by badgerigar; December 16th 2008 at 02:30 PM. Reason: fixed past mistake
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  5. #5
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    thank you i actually got the 1/2 part so i think i'm getting the hang of it
    but inside the parenthesis i had (1)/[(x/2)+1] is that the same thing as what you had?
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  6. #6
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    thank you i actually got the 1/2 part so i think i'm getting the hang of it
    but inside the parenthesis i had (1)/[(x/2)+1] is that the same thing as what you had?
    Yes, assuming you used x instead of my i like this:

    \sum_{x=0}^1\frac{1}{\frac{x}{2}+1}
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  7. #7
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    yes thats what i got, i think i understand it better now thank you for your help
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