## 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 ∫_{a}^{b}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:**∫_{a}^{b}x^{n}dx = x^{n+1}/(n+1) evaluated from a to b when n does not equal -1**Exponential Function:**∫_{a}^{b}e^{x}dx = e^{x}evaluated from a to b**Natural Logarithm:**∫_{a}^{b}ln x dx = x ln x - x evaluated from a to b**Trigonometric Functions:**- ∫
_{a}^{b}sin x dx = -cos x evaluated from a to b - ∫
_{a}^{b}cos x dx = sin x evaluated from a to b - ∫
_{a}^{b}tan x dx = -ln|cos x| evaluated from a to b - ∫
_{a}^{b}sec^{2}x dx = tan x evaluated from a to b

- ∫