# Numerical Integration and Differentiation

Quadratures, double and triple integrals, and multidimensional derivatives

Numerical integration functions can approximate the value of an integral whether or not the functional expression is known:

• When you know how to evaluate the function, you can use `integral` to calculate integrals with specified bounds.

• To integrate an array of data where the underlying equation is unknown, you can use `trapz`, which performs trapezoidal integration using the data points to form a series of trapezoids with easily computed areas.

For differentiation, you can differentiate an array of data using `gradient`, which uses a finite difference formula to calculate numerical derivatives. To calculate derivatives of functional expressions, you must use the Symbolic Math Toolbox™ .

## Fonctions

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 `integral` Numerical integration `integral2` Numerically evaluate double integral `integral3` Numerically evaluate triple integral `quadgk` Numerically evaluate integral — Gauss-Kronrod quadrature `quad2d` Numerically evaluate double integral — tiled method
 `cumtrapz` Cumulative trapezoidal numerical integration `trapz` Trapezoidal numerical integration
 `del2` Discrete Laplacian `diff` Differences and approximate derivatives `gradient` Numerical gradient
 `polyint` Polynomial integration `polyder` Polynomial differentiation