Definite Integral Calculator

Calcualte the definite integral for any function for free!

This tool will calculate the definite integral of the inputed equation.
Enter Equation:
Lower Bound
Upper Bound

How to Calculate a Definite Integral Using Our Definite Integral Calculator

To calculate a definite integral using our definite integral calculator, follow these simple steps:

  • Input the Equation: Enter the function you want to integrate in the designated field. Ensure you use the correct mathematical notation.
  • Specify the Variable: Indicate the variable with respect to which you are integrating, (typically x).
  • Define the Limits of Integration: Enter the lower and upper limits of integration for the definite integral.
  • Click 'Calculate': Once your equation, variable, and limits are entered, click the 'Calculate' button.
  • View the Result: The definite integral calculator will display the integral of the given function within the specified limits.

Remember, the definite integral is a number that represents the area under the curve of a function between two points, and it is represented as the integral of the function over a specific interval.

How to Integrate an Equation Using Integral Formulas

Integrating an equation involves following specific integral formulas. Here are the basic steps:

  • Identify the Type of Function: Determine if the function is a polynomial, trigonometric, exponential, or another type.
  • Select the Appropriate Formula (listed below): Use the corresponding integral formula for the function type. For example, the integral of ax^n is (ax^(n+1))/(n+1) when n does not equal -1.
  • Apply the Formula: Substitute your function into the chosen formula and integrate it over the given interval.

What is a Definite Integral

A definite integral refers to the computation of the area under a curve bounded by two specified points. Unlike an indefinite integral, which provides a family of functions, a definite integral gives a numerical value representing this area. It is a fundamental concept in calculus used for various applications in science and engineering.

  • General Form: A definite integral is expressed as ∫ab f(x) dx, where [a, b] are the limits of integration, and f(x) is the function to be integrated.
  • Area Calculation: The primary application of the definite integral is to calculate the area under a curve between two points.
  • Accumulated Quantity: Definite integrals are also used to find accumulated quantities, such as distance traveled over a time interval.

Integral Formulas List

Here's an expanded list of common integral formulas to assist you when performing integration:

  • Power Rule:ab xn dx = xn+1/(n+1) evaluated from a to b when n does not equal -1
  • Exponential Function:ab ex dx = ex evaluated from a to b
  • Natural Logarithm:ab ln x dx = x ln x - x evaluated from a to b
  • Trigonometric Functions:
    • ab sin x dx = -cos x evaluated from a to b
    • ab cos x dx = sin x evaluated from a to b
    • ab tan x dx = -ln|cos x| evaluated from a to b
    • ab sec2 x dx = tan x evaluated from a to b