Definite Integral Calculator
Calculate definite integrals using Simpson's Rule, Trapezoidal Rule, or Rectangle Method
About this calculator
The Definite Integral Calculator computes the numerical value of definite integrals using three powerful approximation methods: Simpson's Rule, Trapezoidal Rule, and Rectangle Method. This tool is essential for students, engineers, and mathematicians who need to evaluate integrals that are difficult or impossible to solve analytically. It provides accurate numerical approximations by dividing the integration interval into smaller subintervals and applying the selected numerical integration technique to estimate the area under the curve.
How to use
Enter your function in the input field, specify the lower and upper limits of integration, and select your preferred numerical method (Simpson's Rule, Trapezoidal Rule, or Rectangle Method). Choose the number of subintervals for accuracy, then click calculate to get the numerical approximation of your definite integral with step-by-step calculations.
Frequently asked questions
Which numerical integration method is most accurate?
Simpson's Rule is generally the most accurate for smooth functions, followed by the Trapezoidal Rule, then the Rectangle Method. Simpson's Rule provides better approximations with fewer intervals.
How many subintervals should I use for accurate results?
More subintervals increase accuracy but require more computation. Start with 10-20 intervals for basic functions, and increase to 100+ for higher precision or complex functions.
Can this calculator handle all types of functions?
The calculator works with most continuous functions including polynomials, trigonometric, exponential, and logarithmic functions. Discontinuous functions may produce inaccurate results at discontinuity points.