Riemann Sum Calculator (Left, Right, Midpoint, Trapezoid)
Use this free Riemann sum calculator to approximate a definite integral. Choose left endpoints, right endpoints, midpoints, or the trapezoidal rule, set the number of subintervals, and see the value, a graph of the rectangles, and the steps.
How it works
The interval [a, b] is split into n equal pieces of width Δx = (b − a)/n. Each piece contributes its width times a sample height; the method decides which sample point is used.
How to use it
- Enter f(x), the interval a and b, and n.
- Pick the method.
- Press Compute sum to see the value, the rectangles, and the estimated error.
Related: the Integral Calculator and more free math calculators.
Frequently asked questions
Which method is most accurate?
For smooth functions the midpoint and trapezoidal rules are usually far more accurate than left or right endpoints for the same n.
How large can n be?
Up to 100000. The graph draws the rectangles when n is small and just the curve when n is large.
Does it show the error?
Yes — it compares the sum to a fine-grid estimate of the true integral.
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