alaina's blog, 20 Feb 2011

I'm just going to review LRAM, RRAM, MRAM, and TRAP and finding the area between two graphs..
LRAM, RRAM, MRAM and TRAP all circulate around Riemann Sums.
Anyway, LRAM is usually an underestimate; whereas, RRAM is usually an overestimate.
To find LRAM and RRAM, first you need to draw the graph or the number of rectangles within the bounds and figure out your delta X. Then, you need to plug in the numbers at the end of each rectangle within the bounds. This gives you your y-values. From there, for LRAM, you multiply each y-value by delta X except for the last and add them together. For RRAM, you multiply each y-value by delta X except for the first and add them together. These values are over and under estimates.
For the Trapezoidal rule, there are two ways to find it. You can add LRAM and RRAM together and multiply by one half, or you can 1/2 (base 1 + base 2)H where bases are y-values and h is like delta X. This method gets you closer to the true area.
Then, there's the midpoint rule (MRAM). Midpoint uses rectangles but touches at a midpoint. So if your directions say to find the area bounded by 0 and 1 using 1 rectangle, your midpoint would be 1/2. From there, you repeat the steps from LRAM and RRAM.