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Integral Calculator

Evaluate integrals with step-by-step work for common functions used in calculus and engineering.

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What is an Integral Calculator?

An Integral Calculator computes the integral of a mathematical function with respect to a specified variable. Integration is a fundamental concept in calculus that represents the accumulation of quantities, such as areas under curves, volumes, and total change. This tool helps students, engineers, and mathematicians evaluate definite and indefinite integrals quickly.

Types of Integrals

  • Definite Integral: Computes the area under a curve between two specified limits, giving a numerical result.
  • Indefinite Integral: Finds the antiderivative of a function, resulting in a function plus a constant of integration.

How to Use This Calculator

  1. Enter your mathematical function using standard notation (e.g., x^2, sin(x), e^x).
  2. Specify the variable of integration (usually x).
  3. Select whether you want a definite integral with upper and lower limits or an indefinite integral.
  4. View the result with step-by-step solution details.

For related calculus tools, try the Derivative Calculator, Fourier Series Coefficients Calculator, or L'Hopital Rule Calculator.

Frequently Asked Questions

What is the difference between definite and indefinite integrals?

A definite integral computes the area under a curve between specified boundaries and returns a numerical value. An indefinite integral finds the general antiderivative of a function and includes an arbitrary constant C.

What are the basic integration rules?

The basic rules include the power rule, constant multiple rule, sum rule, substitution rule, integration by parts, and trigonometric integrals. Each rule handles different types of functions.

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