> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/ko/mathematics/09-integrals-sums-and-limits.md). # 적분, 합, 그리고 극한 ## 적분 적분 표현식은 다음을 사용하여 추가할 수 있습니다 `\int_{lower}^{upper}` 명령을 사용해. 참고로, 적분 표현식은 인라인 및 디스플레이 수학 모드에서 조금 다르게 보일 수 있습니다. | LaTeX 코드 | 출력 | | ------------------------------------- | -------------------------------------------------------------------------------------- | | `텍스트 안의 적분 \(\int_{a}^{b} x^2 \,dx\)` | ![Example of an integral inside text](/files/5557376034b1d96a1daa682e24b0a9aaca77f17c) | | `\[ \int_{a}^{b} x^2 \,dx \]` | ![Example of an integral](/files/cc9be38eb72590df4559f14ad9a2b09897d87443) | ## 다중 적분 이중/삼중/다중 적분과 순환 적분을 얻으려면 다음을 사용해야 합니다 `amsmath` 및 `esint` (순환 적분용) 패키지. | LaTeX 코드 | 출력 | | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------- | | `latex
\begin{gather*}
\iint_V \mu(u,v) \,du\,dv
\\
\iiint_V \mu(u,v,w) \,du\,dv\,dw
\\
\iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw
\\
\idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k
\end{gather*}
` | ![Example of multiple integrals](/files/08e6a6e2a8b58f62a76d0b4b289162db539a729e) | | `latex
\[
\oint_V f(s) \,ds
\]
` | ![Example of integrals](/files/962de502d40416cea0590502f018ff6d7f232888) | ## 합과 곱 적분과 마찬가지로 합 표현식은 다음을 사용하여 추가할 수 있습니다 `\sum_{lower}^{upper}` 명령을 사용해. | LaTeX 코드 | 출력 | | ------------------------------------------- | ----------------------------------------------------------------------------------------- | | `텍스트 안의 합 $\sum_{n=1}^{\infty} 2^{-n} = 1$` | ![Example of sum expression inside text](/files/7618e13825a8fbf1a1066bdfe50a1723d0cc7b97) | | `\[ \sum_{n=1}^{\infty} 2^{-n} = 1 \]` | ![Example of sum expression](/files/8d642edbe90b7df9fa638de947485a062ecac8e7) | 비슷한 방법으로 다음을 사용하여 일련의 인자들의 곱으로 이루어진 표현식을 얻을 수 있습니다 `\prod_{lower}^{upper}` 명령을 사용해. | LaTeX 코드 | 출력 | | --------------------------------- | ------------------------------------------------------------------------------------------- | | `텍스트 안의 곱 $\prod_{i=a}^{b} f(i)$` | ![Example of limit expression inside text](/files/af772a66f74d63f6827bbc3b389bf5b8de149782) | | `\[ \prod_{i=a}^{b} f(i) \]` | ![Example of limit expression](/files/e950006ae59fb9074fa0869700aff7f0984ecc1d) | ## 극한 극한 표현식은 다음을 사용하여 추가할 수 있습니다 `\lim_{lower}` 명령을 사용해. | LaTeX 코드 | 출력 | | ------------------------------------ | --------------------------------------------------------------------------------- | | `텍스트 안의 극한 $\lim_{x\to\infty} f(x)$` | ![Example of limits inside text](/files/e8824b21aa8e3f4074013f0315912ae871c0b5be) | | `\[ \lim_{x\to\infty} f(x) \]` | ![Example of limits](/files/9cad6e4b0ed5db9ce0a0d94e0d71f2314ac103e6) | ## 예시 다음은 예시 LaTeX 문서입니다: ```latex \documentclass{article} \title{적분, 합 및 극한} \author{Overleaf} \date{} \usepackage{amsmath} \begin{document} \maketitle \section{적분} 텍스트 안의 적분 \(\int_{a}^{b} x^2 dx\). \medskip 동일한 적분을 디스플레이 수식으로 표시하면: \[ \int_{a}^{b} x^2 \,dx \] 그리고 다중 적분: \begin{gather*} \iint_V \mu(u,v) \,du\,dv \\ \iiint_V \mu(u,v,w) \,du\,dv\,dw \\ \iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw \\ \idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k \\ \oint_V f(s) \,ds \end{gather*} \section{합과 곱} 텍스트 안의 합 \(\sum_{n=1}^{\infty} 2^{-n} = 1\). 동일한 합을 디스플레이 수식으로 표시하면: \[ \sum_{n=1}^{\infty} 2^{-n} = 1 \] 텍스트 안의 곱 \(\prod_{i=a}^{b} f(i)\). 동일한 곱을 디스플레이 수식으로 표시하면: \[ \prod_{i=a}^{b} f(i) \] \section{극한} 텍스트 안의 극한 \(\lim_{x\to\infty} f(x)\). 동일한 극한을 디스플레이 수식으로 표시하면: \[ \lim_{x\to\infty} f(x) \] \end{document} ``` [이 예제를 Overleaf에서 열기](https://www.overleaf.com/docs?engine=lualatex\&snip_name=Integrals%2C+Sums+and+Limits\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Ctitle%7BIntegrals%2C+Sums+and+Limits%7D%0A%5Cauthor%7BOverleaf%7D%0A%5Cdate%7B%7D%0A%5Cusepackage%7Bamsmath%7D%0A%0A%5Cbegin%7Bdocument%7D%0A%0A%5Cmaketitle%0A%0A%5Csection%7BIntegrals%7D%0A%0AIntegral+%5C%28%5Cint_%7Ba%7D%5E%7Bb%7D+x%5E2+dx%5C%29+inside+text.%0A%0A%5Cmedskip%0A%0AThe+same+integral+on+display%3A%0A%5C%5B%0A++++%5Cint_%7Ba%7D%5E%7Bb%7D+x%5E2+%5C%2Cdx%0A%5C%5D%0Aand+multiple+integrals%3A%0A%5Cbegin%7Bgather%2A%7D%0A++++%5Ciint_V+%5Cmu%28u%2Cv%29+%5C%2Cdu%5C%2Cdv%0A%5C%5C%0A++++%5Ciiint_V+%5Cmu%28u%2Cv%2Cw%29+%5C%2Cdu%5C%2Cdv%5C%2Cdw%0A%5C%5C%0A++++%5Ciiiint_V+%5Cmu%28t%2Cu%2Cv%2Cw%29+%5C%2Cdt%5C%2Cdu%5C%2Cdv%5C%2Cdw%0A%5C%5C%0A++++%5Cidotsint_V+%5Cmu%28u_1%2C%5Cdots%2Cu_k%29+%5C%2Cdu_1+%5Cdots+du_k%0A%5C%5C%0A++++%5Coint_V+f%28s%29+%5C%2Cds%0A%5Cend%7Bgather%2A%7D%0A%0A%5Csection%7BSums+and+products%7D%0A%0ASum+%5C%28%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D+2%5E%7B-n%7D+%3D+1%5C%29+inside+text.%0A%0AThe+same+sum+on+display%3A%0A%5C%5B%0A++++%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D+2%5E%7B-n%7D+%3D+1%0A%5C%5D%0A%0AProduct+%5C%28%5Cprod_%7Bi%3Da%7D%5E%7Bb%7D+f%28i%29%5C%29+inside+text.%0A%0AThe+same+product+on+display%3A%0A%5C%5B%0A++++%5Cprod_%7Bi%3Da%7D%5E%7Bb%7D+f%28i%29%0A%5C%5D%0A%0A%5Csection%7BLimits%7D%0A%0ALimit+%5C%28%5Clim_%7Bx%5Cto%5Cinfty%7D+f%28x%29%5C%29+inside+text.%0A%0AThe+same+limit+on+display%3A%0A%5C%5B%0A++++%5Clim_%7Bx%5Cto%5Cinfty%7D+f%28x%29%0A%5C%5D%0A%0A%5Cend%7Bdocument%7D) ## 추가 읽을거리 자세한 내용은 다음을 참조하세요 * [수학 표현식](/latex/ko/mathematics/01-mathematical-expressions.md) * [아래첨자와 위첨자](/latex/ko/mathematics/02-subscripts-and-superscripts.md) * [분수와 이항식](/latex/ko/mathematics/05-fractions-and-binomials.md) * [수학 모드의 표시 스타일](/latex/ko/mathematics/10-display-style-in-math-mode.md) --- # Agent Instructions This documentation is published with GitBook. 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