Calculus · INT
Riemann Sums — Approximate Area Under a Curve
Approximate ∫[a,b] f(x) dx by summing n rectangles of width Δx = (b−a)/n with heights at left, right, or midpoints.
CalculusCommon Core LIM-5.AINTVerified correct ✓
Worked examples
Approximate ∫[2,6] (2x + 1) dx using a right-endpoint Riemann sum with n = 4 equal subintervals. Round to 4 decimal places.
Answer: 40
Approximate ∫[1,5] (x² + 3) dx using a midpoint-endpoint Riemann sum with n = 6 equal subintervals. Round to 4 decimal places.
Answer: 53.1852
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