i recently for out a problem asking for the riemann sum of sinx from 0<x<3pi/2 using 3 rectangles with right endpoints. I found that the answer was pi/2 and then the exact area of this was 1. am i right in what i did?

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- Nov 13th 2012, 12:48 PMpnfullerriemann sum
i recently for out a problem asking for the riemann sum of sinx from 0<x<3pi/2 using 3 rectangles with right endpoints. I found that the answer was pi/2 and then the exact area of this was 1. am i right in what i did?

- Nov 13th 2012, 08:03 PMhollywoodRe: riemann sum
The width of your rectangles is $\displaystyle \frac{\pi}{2}$, and the heights are $\displaystyle \sin{\frac{\pi}{2}}=1$, $\displaystyle \sin{\pi}=0$, and $\displaystyle \sin{\frac{3\pi}{2}}=-1$. So the Riemann sum should be:

$\displaystyle \frac{\pi}{2}(1+0+(-1))=0$.

These rectangles are really wide, so you shouldn't expect the result to be close to the actual area, which you have correctly calculated as:

$\displaystyle \int_0^{\frac{3\pi}{2}}\sin{x}\ dx=-\cos{x}|_0^{\frac{3\pi}{2}}=\cos{0}-\cos{\frac{3\pi}{2}}=1-0=1$

- Hollywood