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Math Help - Riemann Sum to an integral

  1. #1
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    Riemann Sum to an integral

    I'm having problem with this problem. I've attached a picture, because I cannot figure out how to simplify this down to typing.

    I've tried just about everything our teacher has taught/shown us, but I'm coming up with wrong answers.
    Attached Thumbnails Attached Thumbnails Riemann Sum to an integral-calcproblem.jpg  
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  2. #2
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    Remember the general form of this:

    \lim_{n->\infty}\Sigma_{k=1}^nf(a+k\Delta x)\Delta x =\int_a^bf(x)dx

    \Delta x=\frac{b-a}{n}

    In this case, the \Delta x=\frac{3}{n} since a=0. In the case that f(x)=sin(x) we have:

    The sin(a+k\Delta x)=sin(k \Delta x)=sin\left(k\frac{3}{n}\right)

    However, you're given sin\left(k\frac{9}{n}\right), so what do you have to do to sin(x) to get sin\left(k\frac{9}{n}\right) instead of sin\left(k\frac{3}{n}\right)?
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  3. #3
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    You could multiply by 3? I just got the answer right after you replied. Thanks though. The way I did it, it didn't really stick in my head. But after reading this I feel like I've learned something. Thanks.
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