Beispiel: Symbolische Integralfunktionen

Symbolische Mathematik > Arbeiten mit symbolischer Mathematik > Analysis > Beispiel: Symbolische Integralfunktionen

Verwenden Sie das Schlüsselwort float, um Funktionen auszuwerten, die nur mit dem symbolischen und nicht mit dem numerischen Gleichheitszeichen ausgewertet werden können.

Ei: exponentielles Integral

1. Verwenden Sie das Schlüsselwort float, um die Funktion Ei bei x=2 numerisch auszuwerten:

2. Werten Sie die komplexe exponentielle Integralfunktion für eine reelle Zahl x aus:

3. Verwenden Sie die Funktion clear, um den vorherigen numerischen und symbolischen Wert von x zu löschen:

4. Verifizieren Sie, dass die folgenden Integrale Antworten in Bezug auf die exponentielle Integralfunktion zurückgeben:

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            <id xml:space="preserve">τ</id>
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            <apply>
              <pow />
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            <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">τ</id>
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        </lambda>
        <lowerBound>
          <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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        <upperBound>
          <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">∞</id>
        </upperBound>
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      <command>
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          <id xml:space="preserve">assume</id>
          <apply>
            <greaterThan />
            <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
            <real>0</real>
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            <div />
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              <pow />
              <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">e</id>
              <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">τ</id>
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          <id xml:space="preserve">assume</id>
          <apply>
            <lessOrEqual />
            <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
            <real>0</real>
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          <neg />
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            <real>0</real>
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            </lambda>
            <id labels="CONSTANT" xml:space="preserve">∞</id>
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                  <apply>
                    <minus />
                    <apply>
                      <mult />
                      <apply>
                        <pow />
                        <id labels="*" xml:space="preserve">c</id>
                        <real>2</real>
                      </apply>
                      <apply>
                        <id labels="FUNCTION" xml:space="preserve">Ei</id>
                        <sequence>
                          <real>1</real>
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                            <mult />
                            <id labels="VARIABLE" xml:space="preserve">τ</id>
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                              <pow />
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                              <real>2</real>
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                          </apply>
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                    </apply>
                    <apply>
                      <div />
                      <apply>
                        <pow />
                        <id labels="CONSTANT" xml:space="preserve">e</id>
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                              <mult />
                              <id labels="VARIABLE" xml:space="preserve">τ</id>
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                                <pow />
                                <id labels="*" xml:space="preserve">c</id>
                                <real>2</real>
                              </apply>
                            </apply>
                          </parens>
                        </apply>
                      </apply>
                      <id labels="VARIABLE" xml:space="preserve">τ</id>
                    </apply>
                  </apply>
                </parens>
              </lambda>
              <real>1</real>
            </apply>
          </parens>
        </apply>
      </symResult>
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Ci: Kosinusintegral

1. Verwenden Sie das Schlüsselwort float, um die Funktion Ci bei x=1 auszuwerten:

2. Verifizieren Sie, dass die folgenden Integrale Antworten in Bezug auf die Kosinusintegralfunktion zurückgeben:

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              <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">cos</id>
              <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">τ</id>
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            <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">τ</id>
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        <lowerBound>
          <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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        <upperBound>
          <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">∞</id>
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      <command>
        <sequence>
          <id xml:space="preserve">assume</id>
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            <greaterThan />
            <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <neg />
          <apply>
            <id labels="FUNCTION" xml:space="preserve">Ci</id>
            <id labels="*" xml:space="preserve">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
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Si: Sinusintegral

1. Verwenden Sie das Schlüsselwort float, um die Funktion Si bei x=2 auszuwerten:

2. Verifizieren Sie, dass die folgenden Integrale Antworten in Bezug auf die Sinusintegralfunktion zurückgeben:

FresnelC: Fresnel-Kosinusintegral

1. Verwenden Sie das Schlüsselwort float, um die Funktion FresnelC bei x=2 auszuwerten:

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        <apply>
          <mult />
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            <mult />
            <real>2</real>
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              <pow />
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                <apply>
                  <div />
                  <real>2</real>
                  <id labels="CONSTANT" xml:space="preserve">π</id>
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              <apply>
                <neg />
                <apply>
                  <div />
                  <real>1</real>
                  <real>2</real>
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            </apply>
          </apply>
          <apply>
            <id labels="FUNCTION" xml:space="preserve">FresnelC</id>
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              <mult />
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                <nthRoot />
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                  <real>2</real>
                  <id labels="CONSTANT" xml:space="preserve">π</id>
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                <nthRoot />
                <placeholder />
                <id labels="*" xml:space="preserve">x</id>
              </apply>
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FresnelS: Fresnel-Sinusintegral

1. Verwenden Sie das Schlüsselwort float, um die Funktion FresnelS bei x=2 auszuwerten:

2. Verifizieren Sie, ob das folgende Integral ein Ergebnis in Bezug auf die Fresnel-Sinus- und -Kosinusintegralfunktionen zurückgibt:

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                        <id labels="*" xml:space="preserve">c</id>
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                        <real>2</real>
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