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Math Help - Upper and Lower Limits of interval for Riemann's Sum

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    Upper and Lower Limits of interval for Riemann's Sum

    So i tried to this question and got f(x) = 1 + x
    upper estimate = 9
    lower estimate = 6

    wondering if i'm on the right path. thx!
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    Quote Originally Posted by simba412 View Post
    So i tried to this question and got f(x) = 1 + x
    upper estimate = 9
    lower estimate = 6
    No.

    The lower limit is \int_0^3 {1dx}

    The upper limit is \int_0^3 {(1+x)dx}
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    ohhh so: lower = 3, upper = 3+3x?
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    Quote Originally Posted by simba412 View Post
    ohhh so: lower = 3, upper = 3+3x?
    not quite ...

    1 \le f(x) \le 1+x

    as Plato stated ...

    \int_0^3 dx \le \int_0^3 f(x) \, dx \le \int_0^3 1+x \, dx

    the lower limit is 3, but the upper limit is not 3 + 3x
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    i thought the upper limit was (1+x)dx where dx = 3, therefore 3(1+x)???
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    oh wait... (1 + (3-0))3 = 12?
    Last edited by simba412; November 18th 2012 at 04:16 PM.
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    ...
    Attached Thumbnails Attached Thumbnails Upper and Lower Limits of interval for Riemann's Sum-sum.png  
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    Re: Upper and Lower Limits of interval for Riemann's Sum

    thanks for the graph. i think i got it! the lower limit represents, in this case, the area of the red rectange. the upper limit represents the the area of the triangle + rectange multiplied by 2 since we take the upper value of x therefore = 4x3 = 12
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