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

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• Apr 23rd 2010, 12:09 AM
ShaXar
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)

Thanks
• Apr 23rd 2010, 03:24 AM
HallsofIvy
Quote:

Originally Posted by ShaXar
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.
• Apr 23rd 2010, 03:56 AM
CaptainBlack
Quote:

Originally Posted by HallsofIvy
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.

CB
• Apr 23rd 2010, 05:34 AM
HallsofIvy
Yes, I was assuming that.