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Math Help - riemann sum

  1. #1
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    riemann sum

    i recently for out a problem asking for the riemann sum of sinx from 0<x<3pi/2 using 3 rectangles with right endpoints. I found that the answer was pi/2 and then the exact area of this was 1. am i right in what i did?
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  2. #2
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    Re: riemann sum

    The width of your rectangles is \frac{\pi}{2}, and the heights are \sin{\frac{\pi}{2}}=1, \sin{\pi}=0, and \sin{\frac{3\pi}{2}}=-1. So the Riemann sum should be:
    \frac{\pi}{2}(1+0+(-1))=0.

    These rectangles are really wide, so you shouldn't expect the result to be close to the actual area, which you have correctly calculated as:
    \int_0^{\frac{3\pi}{2}}\sin{x}\ dx=-\cos{x}|_0^{\frac{3\pi}{2}}=\cos{0}-\cos{\frac{3\pi}{2}}=1-0=1

    - Hollywood
    Last edited by hollywood; November 13th 2012 at 09:04 PM. Reason: Latex fix
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