Rectangular Rule Integration
Approximate definite integrals using the rectangular rule
About this calculator
The Rectangular Rule Integration calculator approximates definite integrals using the rectangular (midpoint) rule method. This numerical integration technique divides the area under a curve into rectangles and sums their areas to estimate the integral value. It's particularly useful when dealing with complex functions that don't have elementary antiderivatives, or when you need quick numerical approximations for engineering, physics, and mathematical applications where exact analytical solutions are difficult to obtain.
How to use
Enter your function in the input field, specify the lower and upper limits of integration, and set the number of rectangles (subdivisions) for accuracy. The calculator will automatically compute the approximate integral value using the rectangular rule method and display the result with the step-by-step calculation process.
Frequently asked questions
What is the rectangular rule in numerical integration?
The rectangular rule approximates integrals by dividing the integration interval into rectangles and using the function value at the midpoint of each rectangle to calculate the area.
How accurate is the rectangular rule method?
Accuracy increases with more subdivisions. The rectangular rule typically provides moderate accuracy and is less precise than Simpson's rule but more accurate than basic left/right endpoint methods.
When should I use rectangular rule integration?
Use it for functions without elementary antiderivatives, quick approximations, or when other numerical methods are unavailable. It's ideal for educational purposes and preliminary calculations.