Difference between revisions of "NIntegral Command"

Latest revision as of 14:54, 18 August 2022

NIntegral( <Function>, <Start x-Value>, <End x-Value> ): Computes (numerically) the definite integral \int_a^bf(x)\mathrm{d}x of the given function f, from a (Start x-Value) to b (End x-Value).; Example: NIntegral(ℯ^(-x^2), 0, 1) yields 0.75.

NIntegral( <Function>, <Start x-Value>, <Start y-Value>, <End x-Value> ): Computes (numerically) the indefinite integral of the given function, and plots the graph of that function through (Start x-Value, Start y-Value), with end point at (End x-Value).; Example: NIntegral(sin(x)/x, π, 1, 2π) plots the graph of the indefinite integral y=F(x)+c of the given function in the interval [π, 2π]. The value of c is defined by the initial condition (start x-Value, start y-Value)=(π, 1).

Hint: In the

CAS View the following syntax can also be used:

NIntegral( <Function>, <Variable>, <Start Value>, <End Value> ): Computes (numerically) the definite integral \int_a^bf(t)\mathrm{d}x of the given function f, from a (Start value) to b (End value), with respect to the given variable.; Example: NIntegral(ℯ^(-a^2), a, 0, 1) yields 0.75.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}}
-{{command|geogebra}}
+;NIntegral( <Function>, <Start x-Value>, <End x-Value> )
-;NIntegral[ <Function>, <Start x-Value>, <End x-Value> ]
+:Computes (numerically) the definite integral <math>\int_a^bf(x)\mathrm{d}x</math> of the given function ''f'', from ''a'' (''Start x-Value'') to ''b'' (''End x-Value'').
-:Let ''a'' be the ''Start x-Value'', ''b'' be the ''End x-Value'' and ''f'' the ''Function''. NIntegral-command computes the definite integral <math>\int_a^bf(x)\mathrm{d}x</math> numerically.
+:{{example| 1=<code><nowiki>NIntegral(ℯ^(-x^2), 0, 1)</nowiki></code> yields ''0.75''.}}
-==CAS Syntax==
-;NIntegral[ <Function>, <Start x-Value>, <End x-Value> ]
-:Let ''a'' be the ''Start x-Value'', ''b'' be the ''End x-Value'' and ''f'' the ''Function''. NIntegral-command computes the definite integral <math>\int_a^bf(x)\mathrm{d}x</math> numerically.
-:{{example| 1=<div><code><nowiki>NIntegral[ℯ^(-x^2), 0, 1]</nowiki></code> yields ''0.746824132812427''.</div>}}
-;NIntegral[ <Function>, <Variable>, <Start Value>, <End Value> ]
+;NIntegral( <Function>, <Start x-Value>, <Start y-Value>, <End x-Value> )
-:Let ''a'' be the ''Start x-Value'', ''b'' be the ''End x-Value'', ''f'' the ''Function'' and ''t'' the ''Variable'' to integrate. NIntegral-command computes the definite integral <math>\int_a^bf(t)\mathrm{d}t</math> numerically.
+:Computes (numerically) the indefinite integral of the given function, and plots the graph of that function through (''Start x-Value'', ''Start y-Value''), with end point at (''End x-Value'').
-:{{example| 1=<div><code><nowiki>NIntegral[ℯ^(-a^2), a, 0, 1]</nowiki></code> yields ''0.746824132812427''.</div>}}
+:{{example| 1=<code><nowiki>NIntegral(sin(x)/x, π, 1, 2π)</nowiki></code> plots the graph of the indefinite integral <math>y=F(x)+c</math> of the given function in the interval [π, 2π]. The value of <math>c</math> is defined by the initial condition (start x-Value, start y-Value)=(π, 1).}}
+{{hint|1=In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] the following syntax can also be used:
+<br>
+;NIntegral( <Function>, <Variable>, <Start Value>, <End Value> )
+:Computes (numerically) the definite integral <math>\int_a^bf(t)\mathrm{d}x</math> of the given function ''f'', from ''a'' (''Start value'') to ''b'' (''End value''), with respect to the given variable.
+:{{example| 1=<code><nowiki>NIntegral(ℯ^(-a^2), a, 0, 1)</nowiki></code> yields ''0.75''.}}
+}}

Difference between revisions of "NIntegral Command"

Latest revision as of 14:54, 18 August 2022

NIntegral

Command Categories (All commands)