This tool will calculate the midpoint rule approximation of an integral for a given function, interval, and number of subintervals.

## Midpoint Rule Calculator

## How to Use the Calculator

To use the Midpoint Rule Calculator, simply enter the function you want to integrate using standard mathematical syntax. For exponentiation, use the caret symbol (^). For example, to enter ( f(x) = 3x^2 ), type “3*x^2”. Next, enter the lower bound (a) and upper bound (b) for the interval over which you want to integrate, followed by the number of subintervals (n).

Once all fields are filled, click on the “Calculate” button. The result will be displayed instantly in the ‘Result’ field.

## How it Calculates the Result

The Midpoint Rule is a numerical method used to estimate the integral of a function. The method works by dividing the interval from ( a ) to ( b ) into ( n ) equal subintervals, finding the midpoint of each subinterval, and then evaluating the function at each midpoint. The sum of these values, multiplied by the width of the subintervals, provides an estimate for the integral of the function.

## Limitations

This calculator utilizes JavaScript’s built-in eval function for mathematical expression evaluation, which can introduce errors if complex expressions or unsupported mathematical functions are entered. In addition, it does not validate inputs, so incorrect inputs could potentially cause incorrect or undefined results. The Midpoint Rule itself is an approximation method and its accuracy depends on how the function behaves on the interval and the number of subintervals chosen; smoother functions and a greater number of subintervals typically yield more accurate results.