\int_{0}^{2} x^2\,dx = 2.6667
left sum 2.1875, exact integral 2.6667, error 0.4792. The left sum is an underestimate here.
left sum, n = 8
2.1875
exact integral
2.6667
error
0.4792
Error (log scale)The left sum is an underestimate here
Full bar is the worst single-rectangle error for this function; empty means the sum is within 0.0001 of the exact integral.
Riemann Sum Slider: Drag n, Watch the Error Vanish from CalcLearn, free AP Calculus study tools.