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Math Help - Upper and Lower expression for f(x)=Sinx

  1. #1
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    Exclamation Upper and Lower expression for f(x)=Sinx

    What are the expressions of Un and Ln (n is the number of small regtangles) for f(x)=sinx on [0,π/2] ?

    (NO need to evaluate these sums)


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  2. #2
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    Quote Originally Posted by ShaXar View Post
    What are the expressions of Un and Ln (n is the number of small regtangles) for f(x)=sinx on [0,π/2] ?

    (NO need to evaluate these sums)


    Thanks
    Do understand what Un and Ln mean? The rest is just arithmetic. Divide the interval from 0 to \pi/2 into n intervals of equal length so that each has length \pi/2n. Since sin(x) is an increasing function on [0, \pi/2], the lowest value in each interval is at the left endpoint, i\pi/2n and the highest value is at the right endpoint, (i+1)\pi/2n with i going from 0 to n-1.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    Do understand what Un and Ln mean? The rest is just arithmetic. Divide the interval from 0 to \pi/2 into n intervals of equal length so that each has length \pi/2n. Since sin(x) is an increasing function on [0, \pi/2], the lowest value in each interval is at the left endpoint, i\pi/2n and the highest value is at the right endpoint, (i+1)\pi/2n with i going from 0 to n-1.
    Riemann sums is my guess.

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  4. #4
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    Yes, I was assuming that.
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