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Thread: 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:

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

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

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

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

    However, you're given $\displaystyle sin\left(k\frac{9}{n}\right)$, so what do you have to do to $\displaystyle sin(x)$ to get $\displaystyle sin\left(k\frac{9}{n}\right)$ instead of $\displaystyle sin\left(k\frac{3}{n}\right)$?
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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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