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Riemann Sum Calculator

Approximate a definite integral with left, right, midpoint, or trapezoidal sums — enter f(x), the interval, and n to see the value, the rectangles, and the steps.

Σ f(x_i) · Δx   with   Δx = (b − a)/n
f(x) a (start) b (end) n (rects)

Use x as the variable. n is the number of subintervals (1–100000). The interval needs a < b.

Results

Riemann sum
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Method
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Δx = (b − a)/n
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Subintervals n
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Approx. exact integral
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Approximation error |sum − integral|
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Graph

f(x)Rectangles / trapezoids

Step-by-step