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Math Help - Riemann sums

  1. #1
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    Riemann sums

    I'm having trouble understanding how to express integrals as the limit of Riemann sums and visa versa. I've attached a picture with the current problem I'm working on if someone wouldn't mind helping me I'd really appreciate it. You can see my current (incorrect) response to the question to get an idea of what I was TRYING to do.
    Attached Thumbnails Attached Thumbnails Riemann sums-picture-1.png  
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  2. #2
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    It is a simple mistake: the 1 should be a 3 as in 3+\frac{4i}{n}
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  3. #3
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    I think all you need is to check your image:




    So take \Delta x=\frac{4}{n} so that {{x}_{i}}=3+\frac{4i}{n}, so

    \int_{3}^{7}{\frac{x}{2+{{x}^{5}}}\,dx}=\underset{  n\to \infty }{\mathop{\lim }}\,\frac{4}{n}\sum\limits_{i=1}^{n}{\frac{3+\dfra  c{4i}{n}}{2+{{\left( 3+\dfrac{4i}{n} \right)}^{5}}}}.

    -- Ahhh, Plato beat me to it.
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  4. #4
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    So it should be a 3 instead of a 1 because the a is 3 and not 1, correct? Just making sure I understand
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  5. #5
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    Never mind this response, wrong thread, lol
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