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積分

定積分と不定積分、積分の数値近似、積分手法

メモ

MuPAD® Notebook は将来のリリースでは削除される予定です。代わりに MATLAB® ライブ スクリプトを使用してください。

MuPAD Notebook ファイルを MATLAB ライブ スクリプト ファイルに変換するには、convertMuPADNotebook を参照してください。MATLAB ライブ スクリプトは、多少の違いはありますが、MuPAD 機能の大半をサポートします。詳細は、MuPAD Notebook を MATLAB ライブ スクリプトに変換を参照してください。

MuPAD 関数

intDefinite and indefinite integrals
int::addpatternAdd patterns for integration
intlib::bypartsIntegration by parts
intlib::changevarChange of variable
intlib::intOverSetIntegration over a set
intlib::printWarningsEnable or disable warnings
numeric::gldataWeights and abscissae of Gauss-Legendre quadrature
numeric::gtdataWeights and abscissae of Gauss-Tschebyscheff quadrature
numeric::intNumerical integration (the Float attribute of Int )
numeric::ncdataWeights and abscissae of Newton-Cotes quadrature
numeric::quadratureNumerical integration ( Quadrature )

例および操作のヒント

Compute Indefinite Integrals

To integrate a mathematical expression f means to find an expression F such that the first derivative of F is f. The expression F is an antiderivative of f. Integration is a more complicated task than differentiation. In contrast to differentiation, there is no general algorithm for computing integrals of an arbitrary expression. When you differentiate an expression, the result is often represented in terms of the same or less complicated functions. When you integrate an expression, the result often involves much more complicated functions than those you use in the original expression. For example, if the original expression consists of elementary functions, you can get the result in terms of elementary functions:

Compute Definite Integrals

For definite integration, the int command restricts the integration variable x to the given range of integration.

Compute Multiple Integrals

To compute multiple integrals, use nested calls to int. For example, compute the surface area and the volume of a sphere using spherical coordinates.

Apply Standard Integration Methods Directly

Integration by parts is one of the common methods for computing integrals. Using this method, you rewrite the original integral in terms of an expression containing a simpler integral. Integration by parts for indefinite integrals uses the definition:

Get Simpler Results

When computing integrals, MuPAD applies strict mathematical rules. For example, integrate the following expression:

If an Integral Is Undefined

Handling undefined integrals.

If MuPAD Cannot Compute an Integral

If the int command cannot compute a closed form of an integral, MuPAD returns an unresolved integral:

概念

Integration Utilities

Use only in the MuPAD Notebook Interface. This functionality does not run in MATLAB.

Numeric Algorithms Library

Use only in the MuPAD Notebook Interface. This functionality does not run in MATLAB.