I am trying to figure out these questions and I think I understand how this complicated formula works. I do not have it memorized but I do have it written down for reference.
If $f(x)=e^x-2$, $0\le x\le2$ then find the Riemann sum with $n=4$ correct to six decimal places, taking the sample points to be midpoints. What does the riemann sum represent? Illustrate with a diagram.
I get $.5(f(.5)+f(1)f(1.5)f(2))$ which is the incorrect answer. What am I doing wrong? To find $\Delta x$ I subtract the beginning from the end which is 2 and divide by the number of intervals which is 4 which gives .5 which is what I used but gave me an incorrect answer.
Best Answer
Your $\Delta x$ is correct, but your midpoints are not.
Your intervals are $[0,0.5],[0.5,1],[1,1.5],[1.5,2]$.
That means the midpoints will be $0.25,0.75,1.25,$ and $1.75$.
You also left out some plus signs in your expression, but I think that was just a typo?