* Bug 16145 fixed: intg() integrate() intc() default atol
[scilab.git] / scilab / modules / differential_equations / help / pt_BR / integrate.xml
index 1f262e9..ff4ccf9 100644 (file)
@@ -2,8 +2,8 @@
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
- *
  * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
  *
  * This file is hereby licensed under the terms of the GNU GPL v2.0,
  * pursuant to article 5.3.4 of the CeCILL v.2.1.
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="integrate" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="integrate" xml:lang="pt">
     <refnamediv>
         <refname>integrate</refname>
         <refpurpose>integração pela quadratura</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>x=integrate(expr,v,x0,x1 [,atol [,rtol]])</synopsis>
+        <synopsis>
+          y = integrate(expr, v, x0, x1)
+          y = integrate(expr, v, x0, x1, atol)
+          y = integrate(expr, v, x0, x1, atol, rtol)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
             <varlistentry>
                 <term>expr</term>
                 <listitem>
-                    <para>string definindo uma expressão Scilab</para>
+                    string definindo uma expressão Scilab.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>v</term>
                 <listitem>
-                    <para>string (variável da integração) </para>
+                    string : variável da integração.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>x0</term>
                 <listitem>
-                    <para>número real (limite inferior de integração) </para>
+                    número real : limite inferior de integração.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>x1</term>
                 <listitem>
-                    <para>vetor de números reais, limites superiores de
-                        integração
-                    </para>
+                    vetor de números reais : limites superiores de integração.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>atol</term>
                 <listitem>
-                    <para>número real (erro absoluto). Valor padrão: 1.-8</para>
+                    número real : erro absoluto. Valor padrão: 1e-13.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>rtol</term>
                 <listitem>
-                    <para>número real (erro relativo). Valor padrão: 1e-14</para>
+                    número real : erro relativo. Valor padrão: 1e-8.
+                    <para/>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>x</term>
+                <term>y</term>
                 <listitem>
-                    <para>vetor de números reais, o valor da integral para cada
-                        <literal>x1(i)</literal>.
-                    </para>
+                    vetor de números reais : o valor da integral para cada <literal>x1(i)</literal>.
+                    <para/>
                 </listitem>
             </varlistentry>
         </variablelist>
     <refsection>
         <title>Descrição</title>
         <para>
-            Computa :
-            <subscript>
-                <inlinemediaobject>
-                    <imageobject>
-                        <imagedata>
-                            <mml:math display="block" scilab:localized="true">
-                                <mml:mi mathvariant="normal">x</mml:mi>
-                                <mml:mrow>
-                                    <mml:mrow>
-                                        <mml:mo>(</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mo>)</mml:mo>
-                                    </mml:mrow>
-                                    <mml:mo>=</mml:mo>
-                                    <mml:mrow>
-                                        <mml:msubsup>
-                                            <mml:mo>∫</mml:mo>
-                                            <mml:msub>
-                                                <mml:mi mathvariant="normal">x</mml:mi><mml:mn>0</mml:mn>
-                                            </mml:msub>
-                                            <mml:mrow>
-                                                <mml:msub>
-                                                    <mml:mi mathvariant="normal">x</mml:mi><mml:mn>1</mml:mn>
-                                                </mml:msub>
-                                                <mml:mrow>
-                                                    <mml:mo>(</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mo>)</mml:mo>
-                                                </mml:mrow>
-                                            </mml:mrow>
-                                        </mml:msubsup>
-                                        <mml:mi mathvariant="normal">f</mml:mi>
-                                    </mml:mrow>
-                                </mml:mrow>
-                                <mml:mrow>
-                                    <mml:mo>(</mml:mo><mml:mi mathvariant="normal">v</mml:mi><mml:mo>)</mml:mo>
-                                </mml:mrow>
-                                <mml:mi>d</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:annotation mml:encoding="StarMath 5.0">x(i)=int_{x_0}^{x_1(i)}
-                                    f(v)dv
-                                </mml:annotation>
-                            </mml:math>
-                        </imagedata>
-                    </imageobject>
-                </inlinemediaobject>
-            </subscript>
-            para
-            <literal>i=1:size(x1,'*')</literal>
-        </para>
-        <para>
-            Onde
-            <inlinemediaobject>
-                <imageobject>
-                    <imagedata>
-                        <mml:math display="block">
-                            <mml:mi mathvariant="normal">f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">v</mml:mi><mml:mo>)</mml:mo>
-                        </mml:math>
-                    </imagedata>
-                </imageobject>
-            </inlinemediaobject>
-            é dado pela expressão
-            <literal>expr</literal>.
+            Computa
+            <latex alt="y(i) = integral_{x_0}^{x_1(i)} f(v).dv">
+                y(i) = \int_{x_0}^{x_1(i)} f(v)\,dv
+            </latex>
+            para <literal>i=1:size(x1,'*')</literal>, onde <emphasis>f(v)</emphasis> é dado
+            pela expressão <literal>expr</literal>.
         </para>
         <para>A avaliação procura satisfazer à seguinte precisão:
-            <literal>abs(I-x)&lt;= max(atol,rtol*abs(I))</literal> onde I é o valor
+            <literal>abs(I-y) &lt;= max(atol, rtol*abs(I))</literal> onde I é o valor
             exato da integral.
         </para>
-    </refsection>
-    <refsection>
-        <title>Restrição</title>
-        <para>A expressão dada não deve utilizar nomes de variáveis começando por
-            <literal>%</literal>.
+        <para>
+            <warning>
+                Restrição : A expressão dada não deve utilizar nomes de variáveis começando por
+                <literal>%</literal>.
+            </warning>
         </para>
     </refsection>
     <refsection>
         <title>Exemplos</title>
         <programlisting role="example"><![CDATA[
-x0=0;x1=0:0.1:2*%pi;
-X=integrate('sin(x)','x',x0,x1);
-norm(cos(x1)-(1-X))
+x1 = 0:0.1:2*%pi;
+Y = integrate('sin(x)', 'x', 0, x1);
+norm(cos(x1)-(1-Y))
 
-x1=-10:0.1:10;
-X=integrate(['if x==0 then 1,';
-  'else sin(x)/x,end'],'x',0,x1)
+x1 = -10:0.1:10;
+Y = integrate(['if x==0 then 1,';
+               'else sin(x)/x,end'], 'x', 0, x1)
  ]]></programlisting>
     </refsection>
     <refsection>
@@ -174,4 +133,16 @@ X=integrate(['if x==0 then 1,';
             </member>
         </simplelist>
     </refsection>
+    <refsection role="history">
+        <title>Histórico</title>
+        <revhistory>
+            <revision>
+                <revnumber>6.1.0</revnumber>
+                <revdescription>
+                    Default atol value increased from
+                    10<superscript>-14</superscript> to 10<superscript>-13</superscript>.
+                </revdescription>
+            </revision>
+        </revhistory>
+    </refsection>
 </refentry>