Mathematical Methods · numerical integration · manipulative

Rectangle sums → the definite integral

Pick left, midpoint, or right rectangles. Change the integral and n — watch the sum chase the true area.

y = f(x) Rectangles Exact area

Axes fit to [a, b] · scroll zoom · drag pan · Shift+drag an axis to dilate

Rectangle rule

Subintervals

8

Integral parameters

0
1
1

Limits a,b and shape parameter c reshape the integrand.

Estimate vs reference

Rectangle sum
Exact area

Show on graph

Exact area
shaded region under y = f(x)

Formula