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

1. ## 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

2. 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 $\displaystyle \pi/2$ 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.

3. Originally Posted by HallsofIvy
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.
Riemann sums is my guess.

CB

4. Yes, I was assuming that.