Calc 2 Riemann Sums

Formulas for different Riemann Sums and Steps

Left Riemann sums approximation

-Find Δx by subtracting b-a and dividing by n=number of subintervals.

-Find f(a) to f(b-Δx)

-Add all of the values and multiply by the Δx

Right Riemann sums approximation

-Find Δx by subtracting b-a and dividing by n=number of subintervals

-Find f(a+Δx) to f(b)

-Add all of the values and multiply by Δx

Midpoint rule

-Find Δx by subtracting b-a and dividing by n=number of subintervals

-Draw a diagram of the number line showing the range and subintervals

-Find the midpoint y points. Add (Δx)/2 to A. Then continue to add just Δx to that value and get n values

-Find Δx (f(A + (Δx)/2) + f(previous x value + Δx)… f(b-Δx)

Trapezoid rule

-Find Δx by subtracting b-a and dividing by n=number of subintervals

-DONT multiply the first and last value with 2

-Formula = (Δx)/2) ((f(a) + 2(f(a+Δx)) + 2(f(previous value +Δx) +… + f(b)