Interpret a definite integral as a limit of Riemann sums. Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.

### Examples

*Example*: Find the values of the Riemann sums over the interval [0,1] using 12 and 24 subintervals of equal width for

*f(x)=e*evaluated at the midpoint of each subinterval. Write an expression for the Riemann sums using n intervals of equal width. Find the limit of this Riemann Sums as n goes to infinity.

^{x}*Example*: Estimate

*sin x dx*using a Riemann midpoint sum with 4 subintervals.

*Example*: Find an approximate value for using 6 rectangles of equal width under the graph of *f(x)=x ^{2}* between x=0 and x=3. How did you form your rectangles? Compute this approximation three times using at least three different methods to form the rectangles.

General Information

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Calculus

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

This benchmark is part of these courses.

1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

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