Riemann Sum Calculator
Calculate Riemann sums to approximate definite integrals using left, right, midpoint, or trapezoidal methods.
Function
∫f(x) = x² dx from 0 to 2
2.28000000
Δx = 0.200000
Exact Value
2.66666667
Error
3.8667e-1
All Methods Comparison
Left Sum2.280000
Right Sum3.080000
Midpoint2.660000
Trapezoidal2.680000
Rectangle Data (first 10)
i=1x: [0.0000, 0.2000]
i=2x: [0.2000, 0.4000]
i=3x: [0.4000, 0.6000]
i=4x: [0.6000, 0.8000]
i=5x: [0.8000, 1.0000]
i=6x: [1.0000, 1.2000]
i=7x: [1.2000, 1.4000]
i=8x: [1.4000, 1.6000]
i=9x: [1.6000, 1.8000]
i=10x: [1.8000, 2.0000]
Riemann Sum Methods
Left/Right Sums
Use left or right endpoints of each subinterval to determine rectangle heights.
Midpoint Rule
Uses the midpoint of each subinterval. Generally more accurate than left/right.