Examples for


Integrals come in two varieties: indefinite and definite. Indefinite integrals can be thought of as antiderivatives, and definite integrals give signed area or volume under a curve, surface or solid. Wolfram|Alpha can compute indefinite and definite integrals of one or more variables, and can be used to explore plots, solutions and alternate representations of a wide variety of integrals.

Indefinite Integrals

Find the antiderivatives of mathematical expressions.

Compute an indefinite integral:

Compute an indefinite integral that cannot be expressed in elementary terms:

Generate a table of integrals that contain a given function:

Multiple Integrals

Calculate definite nested integrals in multiple variables.

Compute a multiple integral:

Compute an integral over an unbounded region:

Integrals Related to Special Functions

Find definite or indefinite integrals involving a particular special function.

Explore interesting indefinite integrals containing special functions:

Explore interesting definite integrals containing special functions:

Definite Integrals

Find integrals with lower and upper limits, also known as Riemann integrals.

Compute a definite integral:

Compute an improper integral:

Generate a table of definite integral formulas:

Numerical Integration

Integrate expressions using numerical approximation.

Numerically integrate functions that cannot be integrated symbolically:

Approximate an integral using a specified numerical method:

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