Midpoint Riemann Sums
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Midpoint Riemann Sums means the top-midpoint of the rectangles line up with the function.
Scenario: Given the function and its corresponding graph below, estimate the area under the curve from x = 0 to x = 20 using Midpoint Riemann Sums with 4 rectangles.
PRO TIP: We're using Midpoint Riemann Sums here, so the top midpoint of the rectangles will border the function!
base = b - a / n
b is the upper bound of x = 20.
a is the lower bound of x = 0.
n is the number of rectangles we're using, which is 4.
base = 20 - 0 / 4
base = (20) / 4
base = 5
Answer: Using Midpoint Riemann Sums with 4 rectangles, we can estimate the area under f(x) from x = 0 to x = 20 to be 165.625.