적분을 기호 연산으로 계산하기

기호 > 기호 작업 > 미적분 > 적분을 기호 연산으로 계산하기

적분을 기호 연산으로 계산하기

1. 적분 연산자를 삽입합니다.

2. 적분 기호 오른쪽에 있는 자리 표시자에 식을 입력합니다.

3. 기호 d 오른쪽에 있는 자리 표시자에 적분 변수 x를 입력합니다.

4. 기호 연산 연산자를 삽입합니다.

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              <real>2</real>
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기호 연산 연산자로는 부정 적분만 계산할 수 있습니다.

5. 0부터 5까지 동일한 함수의 정적분을 구하려면 적분의 아래쪽 자리 표시자에 0을 입력하고, 위쪽 자리 표시자에 5를 입력한 다음 2-4단계를 반복합니다.

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              <real>2</real>
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              <pow />
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
            </apply>
          </apply>
        </lambda>
        <lowerBound>
          <real>0</real>
        </lowerBound>
        <upperBound>
          <real>5</real>
        </upperBound>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
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          <minus />
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            <real>17</real>
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              <id xml:space="preserve" labels="CONSTANT">e</id>
              <real>5</real>
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          <real>2</real>
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6. 한계 중 하나 이상이 정의되지 않은 변수일 때 동일한 함수의 정적분 값을 구하려면 2-4단계를 반복합니다. 그 다음 적분의 하한과 상한을 삽입합니다.

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              <pow />
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
              <real>2</real>
            </apply>
            <apply>
              <pow />
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
            </apply>
          </apply>
        </lambda>
        <lowerBound>
          <real>0</real>
        </lowerBound>
        <upperBound>
          <id xml:space="preserve">t</id>
        </upperBound>
      </apply>
      <command>
        <placeholder />
      </command>
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                    <id xml:space="preserve" labels="VARIABLE">t</id>
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                <real>2</real>
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            <apply>
              <pow />
              <id xml:space="preserve" labels="CONSTANT">e</id>
              <id xml:space="preserve" labels="VARIABLE">t</id>
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          <real>2</real>
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극한이 하나 이상 정의되지 않은 정적분 평가 시 기호 엔진은 상한값이 하한값보다 크다고 가정합니다.

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              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
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          </apply>
        </lambda>
        <lowerBound>
          <id xml:space="preserve">a</id>
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        <upperBound>
          <id xml:space="preserve">b</id>
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                <real>2</real>
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                    <id xml:space="preserve" labels="VARIABLE">a</id>
                    <real>2</real>
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                </apply>
                <real>2</real>
              </apply>
            </parens>
            <apply>
              <pow />
              <id xml:space="preserve" labels="CONSTANT">e</id>
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7. 기호 연산의 결과를 함수에 지정하려면 다음과 같이 함수를 정의합니다.

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            <real>2</real>
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코쉬 주 값

(a,b) 구간에서 c 점에 대한 적분의 코쉬 주 값은 다음 식으로 정의됩니다.

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                  <id xml:space="preserve">c</id>
                  <id xml:space="preserve">ε</id>
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              <upperBound>
                <id xml:space="preserve">b</id>
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        </parens>
      </lambda>
      <real>0</real>
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코쉬 주 값의 용도는 f 함수가 c에서 특이점을 가질 때 적분 값을 정의하는 것입니다. 예를 들어 다음 적분은 c=0에서 특이점을 가지므로 기호 연산이 오류를 반환합니다.

이 식을 복사하려면 클릭

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              <real>3</real>
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          </apply>
        </lambda>
        <lowerBound>
          <real>-1</real>
        </lowerBound>
        <upperBound>
          <real>1</real>
        </upperBound>
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      <command>
        <placeholder />
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      <symResult>
        <id xml:space="preserve" labels="*">undefined</id>
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적분의 코쉬 주 값을 구하려면 cauchy 수정자를 추가합니다.

이 식을 복사하려면 클릭

cauchy 키워드를 지정하지 않으면 코쉬 분석이 필요한 적분의 기호 연산은 undefined의 결과를 반환합니다.

관련 항목

기호 미적분 정보

도함수를 기호 연산으로 계산하기

코쉬 분포

예제: 기호 미적분 I

예제: 기호 미적분 II

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