Finding the area..

Feb 2010
98
0
Ok I'm studying for my final looking over my old tests and I can't remember how I got this one right. I tried going from 0, to pi/2, to pi/4, to 3pi/4, to pi using sinx to plug in each but I'm not getting the right answer. Help would be appreciated.

Find the area under the graph of f(x)=sinx from x=0 to x=pi, using the four rectangles with the sample points to be the left endpoints. The answer = 1.896
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Ok I'm studying for my final looking over my old tests and I can't remember how I got this one right. I tried going from 0, to pi/2, to pi/4, to 3pi/4, to pi using sinx to plug in each but I'm not getting the right answer. Help would be appreciated.

Find the area under the graph of f(x)=sinx from x=0 to x=pi, using the four rectangles with the sample points to be the left endpoints. The answer = 1.896
\(\displaystyle \frac{\pi - 0}{4} \left[\sin(0) + \sin\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{2}\right) + \sin\left(\frac{3\pi}{4}\right) \right]\)