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
I think you're relying too much on the formula. Actually think about what you are doing. You are approximating the area under a curve by subdividing it into rectangles and adding up the areas of all the rectangles. The length of each rectangle is the same as the length of each subdivision, and the width of each rectangle is the value of the function at the left-hand endpoint. So that means the area of each rectangle is , where is the left-hand endpoint. Remembering that your interval is a unit in length, that means your approximation is
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'.