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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

Trapezoidal Rule Calculator

Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.

Lower Limit (a)

Upper Limit (b)

Number of Subintervals

Average Trapezoid Height

Key differences

	Rectangular Rule Integration	Trapezoidal Rule Calculator
Category	Calculus	Calculus
Inputs required	4	4
Result	Approximate Integral	Approximate Integral
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 function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.