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Both calculators run independently — change the inputs on either side to compare results.

Rectangular Rule Integration

Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.

Lower Bound (a)

Upper Bound (b)

Number of Intervals (n)

Average Function Value

Calculus

Riemann Sum Calculator

Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums. Use this to understand numerical integration and error in calculus courses.

Function Coefficient

Power of x

Lower Bound

Upper Bound

Number of Subintervals

Riemann Sum Method

Key differences

	Rectangular Rule Integration	Riemann Sum Calculator
Category	Calculus	Calculus
Inputs required	4	6
Result	Approximate Integral	Riemann Sum Approximation
What it does	Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.	Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums. Use this to understand numerical integration and error in calculus courses.