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Math Help - Finding original intergral from given Reimann sum...

  1. #1
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    Finding original intergral from given Reimann sum...

    Hello,

    If possible, may someone take a look at the problem below (note my answers).

    I am not sure why but I only get the first part right (my answer is seven (7).

    Thanks.


    Regards,
    Chris K.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The terms of a Riemann Sum are f(xk)deltax

    deltax = 2/n

    x0 = 5

    x1 = 5 +2/n

    xk = 5 +2k/n

    f(xk) = sqrt(8 + 2k/n) so f(x) = sqrt(3 + 5+2k/n)

    f(x) = sqrt( 3 +x)
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    The terms of a Riemann Sum are f(xk)deltax

    deltax = 2/n

    x0 = 5

    x1 = 5 +2/n

    xk = 5 +2k/n

    f(xk) = sqrt(8 + 2k/n) so f(x) = sqrt(3 + 5+2k/n)

    f(x) = sqrt( 3 +x)
    Thanks!
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  4. #4
    MHF Contributor Calculus26's Avatar
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    so do you also see why g(x) = sqrt(x) with c = 10 ?
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  5. #5
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    Quote Originally Posted by Calculus26 View Post
    so do you also see why g(x) = sqrt(x) with c = 10 ?
    I see that g(x) would be the new limits should g(x) be the anti-derivate of f(x).

    Am I correct?
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  6. #6
    MHF Contributor Calculus26's Avatar
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    No g(x) is simply a horizontal shift of f(x) to the right 3 units

    If you compute the integrals you get the same results as the area doesn't change.

    See attachment
    Attached Thumbnails Attached Thumbnails Finding original intergral from given Reimann sum...-integral3.jpg  
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