riemann sum

**pnfuller** · November 13th 2012, 12:48 PM

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?

**hollywood** · November 13th 2012, 08:03 PM

The width of your rectangles is $\frac{\pi}{2}$ , and the heights are $\sin{\frac{\pi}{2}}=1$ , $\sin{\pi}=0$ , and $\sin{\frac{3\pi}{2}}=-1$ . So the Riemann sum should be:
$\frac{\pi}{2}(1+0+(-1))=0$ .

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

- Hollywood

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