You have forgotten about f(-0.5) in your 12RE.
I'm trying to get an area approximation under the graph, from to by using 6 and 12 left, right, and midpoint rectangles. I've computed 6 LE and 6 & 12 for both the RE and MP rectangles but I can't figure out how to correctly do 12 rectangles for LE and MP rectangles. I already know I got the right answer for the ones I mentioned, but I can't figure out what I'm doing wrong for 12 LE and 12 MP rectangles.
for 6 rectangles, and for 12 rectangles.
I'll write out all my summations that I used my calculator for. I marked the incorrect calculations with **
6 LE is 222
**12 LE ... I got 182.875
6 RE is 474
12 RE is 402
6 MP is 330
**12 MP ... I got 225.328125
Oh that makes a lot more sense. Also, in the graph that I attached, does it look like there are any points on it where f(x) is 0? What confuses me is I've seen some videos on YouTube doing this approximations and certain x values would be skipped because the rectangle had no height (no area) at that point.
I tried to do this to compute the left hand sum with 12 rectangles. where since
And then I basically expanded the summation out
I know that's a lot to look at, but I basically just plug into f(xi) ... Does this look like the proper method to find the area under the curve of the function I listed originally
My mistake. I'm not sure why I thought you were Plato...
The 12 MP approximation came out to be ... It's so much easier to find a starting point and ending point on a graph and then just add the 'change in x'.