MathLiveRiemann sum
A Riemann sum approximates the definite integral of a function by adding up the areas of rectangles whose widths are the subinterval lengths and whose heights are the function values at sample points. It is used to estimate integrals numerically and to define the integral itself.
\sum_{i=1}^{N} (t_i - t_{i-1}) f(t_i)What the symbols mean
| index of the subinterval, running from 1 to N | |
| the function being integrated | |
| number of subintervals | |
| partition points of the interval, with t_0 at the lower limit and t_N at the upper limit | |
| width of the i-th subinterval | |
| value of the function at the sample point t_i |
About this formula
- FieldMathematics
- TopicIntegral calculus
- LevelUniversity
- Also calledRiemann sum formula, approximate integral with rectangles, right endpoint Riemann sum, numerical integration sum, definite integral approximation, rectangle approximation of area under curve
- SourceWikidata Q1156903
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