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Math Help - Trapezoid Rule

  1. #1
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    Trapezoidal Rule

    Estimate the surface are of the figure below using the Trapezoidal Rule.

    I did:
    (40-0)/(2(4))[6+2(5)+2(4)+2(5)+5]
    5[39]=195 ft^2
    The thing is, apparently the correct answer is 250 ft^2 and I don't know why.

    Any help is greatly appreciated
    Last edited by Naples; August 31st 2009 at 09:47 PM.
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  2. #2
    Super Member Matt Westwood's Avatar
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    Can you explain the source of the formula you are using - I'm confused by the 40-0/2(4) bit at the start, and how you got that to equal 5.

    Also, I suspect that what you've done is ignored the bits at the ends - but I don't know how you were told to estimate those.
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  3. #3
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    Quote Originally Posted by Matt Westwood View Post
    Can you explain the source of the formula you are using - I'm confused by the 40-0/2(4) bit at the start, and how you got that to equal 5.

    Also, I suspect that what you've done is ignored the bits at the ends - but I don't know how you were told to estimate those.
    Well the trapezoidal rule formula is ((b-a)/2n)[f(x0) + f(x1) + f(x2) +...+ f(xn-1) + f(xn)]
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  4. #4
    Member eXist's Avatar
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    That's cause you have the rule wrong:

    (\frac{b-a}{2n})[f(x_0) + 2f(x_1) + 2f(x_2) +...+ 2f(x_{n-1}) + f(x_n)]

    Trapezoidal rule - Wikipedia, the free encyclopedia

    It should be twice every inner term like I have written.
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  5. #5
    Super Member Matt Westwood's Avatar
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    Okay, gotcha - I was confused by the dodgy bracketing in the first posting.

    So, I suspect what you've done is ignored the bits at the end. Estimate them as trapezoids from 0 to 6 and from 5 to 0 and make them 10 wide, I suppose.
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  6. #6
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    Yes. The distance from the left vertical line to the right vertical line is 40 but it looks like the entire region goes from 0 to 60. (The "trapezoids" on the left and right will be triangles. If it were me, instead of using the "trapezoid rule" formula, I would estimate the areas of the four trapezoids and two triangles involved and add them. Doing that I get 250.)
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  7. #7
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    Thanks for the help guys, I tried it the way HallsofIvy said and also got 250 so I'm going to stick with that.
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