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

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- Apr 23rd 2010, 12:09 AMShaXarUpper 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)

Thanks - Apr 23rd 2010, 03:24 AMHallsofIvy
Do understand what Un and Ln mean? The rest is just arithmetic. Divide the interval from 0 to $\displaystyle \pi/2$ into n intervals of equal length so that each has length $\displaystyle \pi/2n$. Since sin(x) is an increasing function on $\displaystyle [0, \pi/2]$, the lowest value in each interval is at the left endpoint, $\displaystyle i\pi/2n$ and the highest value is at the right endpoint, $\displaystyle (i+1)\pi/2n$ with i going from 0 to n-1.

- Apr 23rd 2010, 03:56 AMCaptainBlack
- Apr 23rd 2010, 05:34 AMHallsofIvy
Yes, I was assuming that.