What functions can I enter?

You can use standard expressions: x^2, sqrt(x), sin(x), cos(x), tan(x), exp(x) or e^x, ln(x), log(x), abs(x), and combinations with +, -, *, /, ^ and parentheses.

How accurate is the midpoint rule?

The midpoint rule has second-order accuracy — the error is proportional to h^2 (where h = (b-a)/n). Doubling n reduces the error by roughly four times. It is generally more accurate than the trapezoidal rule for smooth functions.

What is the midpoint rule formula?

M_n = h * (f(x_1) + f(x_2) + ... + f(x_n)), where h = (b-a)/n and x_i = a + (i - 0.5) * h is the midpoint of the i-th subinterval.

What is the maximum number of subintervals?

This calculator supports up to 1000 subintervals. Higher values give better accuracy but the table will only display the first 200 rows for readability.

Why does my result say NaN or error?

This usually means the function is undefined at a midpoint (e.g. ln(x) when a subinterval midpoint is ≤ 0, or division by zero). Check your bounds and function.

Midpoint Rule Calculator

Name: Midpoint Rule Calculator
Availability: InStock
Author: Nham Vu

Approximate a definite integral using the midpoint rule — enter your function, bounds, and number of subintervals to get the sum table and result.

Parameters

Function f(x)

Supports: +, -, *, /, ^, sin, cos, tan, exp, ln, sqrt, abs

Lower bound (a)

Upper bound (b)

Subintervals (n)

1 – 1000. Table shows first 200 rows.

Function reference

x^2 x*sin(x) sqrt(x) sin(x) cos(x) tan(x) exp(x) e^x ln(x) log(x) abs(x) 1/(1+x^2)

Subinterval Table

i	Subinterval [a_i, b_i]	Midpoint x_i	f(x_i)

Enter a function and click Calculate to see the approximation.

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Summary