> 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/tr/matematik/09-integrals-sums-and-limits.md). # İntegraller, toplamlar ve limitler ## İntegraller İntegral ifadesi şu kullanılarak eklenebilir `\int_{lower}^{upper}` komutunu. Not, integral ifadesi satır içi ve gösterim matematik modunda biraz farklı görünebilir. | LaTeX kodu | Çıktı | | ------------------------------------------------- | -------------------------------------------------------------------------------------- | | `Metin içinde integral \(\int_{a}^{b} x^2 \,dx\)` | ![Example of an integral inside text](/files/38600480858fd8215cd6e3562a4285a4973908c2) | | `\[ \int_{a}^{b} x^2 \,dx \]` | ![Example of an integral](/files/577321f31bb937a503aafb383b3a5bbb952f1894) | ## Çoklu integraller Çift/üçlü/çoklu integraller ve çevrimsel integraller elde etmek için şu kullanılmalıdır `amsmath` ve `esint` (çevrimsel integraller için) paketleri. | LaTeX kodu | Çıktı | | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------- | | `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/4b7833b688a0cc1e8723101f16a5c5e29b01c6f1) | | `latex
\[
\oint_V f(s) \,ds
\]
` | ![Example of integrals](/files/7a6b4d37d6d840e0cac692d2639e6fc16152692e) | ## Toplamlar ve çarpımlar İntegral gibi, toplam ifadesi de şu kullanılarak eklenebilir `\sum_{lower}^{upper}` komutunu. | LaTeX kodu | Çıktı | | ------------------------------------------------------ | ----------------------------------------------------------------------------------------- | | `Metin içinde toplam $\sum_{n=1}^{\infty} 2^{-n} = 1$` | ![Example of sum expression inside text](/files/bbbced4df28fc491862d99396ef3a60c812d0897) | | `\[ \sum_{n=1}^{\infty} 2^{-n} = 1 \]` | ![Example of sum expression](/files/bedc2c9998a21a2d3b197a165b088b6162276460) | Benzer şekilde, bir dizi çarpanın çarpımıyla ifade şu kullanılarak elde edilebilir `\prod_{lower}^{upper}` komutunu. | LaTeX kodu | Çıktı | | -------------------------------------------- | ------------------------------------------------------------------------------------------- | | `Metin içinde çarpım $\prod_{i=a}^{b} f(i)$` | ![Example of limit expression inside text](/files/b3fc5a43120d5346cec7b54cac43b9d049220771) | | `\[ \prod_{i=a}^{b} f(i) \]` | ![Example of limit expression](/files/b4ac334ca24e91231304a5ef46274dba8133de72) | ## Limitler Limit ifadesi şu kullanılarak eklenebilir `\lim_{lower}` komutunu. | LaTeX kodu | Çıktı | | --------------------------------------------- | --------------------------------------------------------------------------------- | | `Metin içinde limit $\lim_{x\to\infty} f(x)$` | ![Example of limits inside text](/files/b62add6714bb031817d11726b8b7fcec954729a5) | | `\[ \lim_{x\to\infty} f(x) \]` | ![Example of limits](/files/b24393c9b113d2bbe587d4fb2c291bcd29690fc7) | ## Örnekler İşte örnek bir LaTeX belgesi: ```latex \documentclass{article} \title{İntegraller, Toplamlar ve Limitler} \author{Overleaf} \date{} \usepackage{amsmath} \begin{document} \maketitle \section{İntegraller} Metin içinde integral \(\int_{a}^{b} x^2 dx\). \medskip Aynı integral gösterimde: \[ \int_{a}^{b} x^2 \,dx \] ve çoklu integraller: \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{Toplamlar ve çarpımlar} Metin içinde toplam \(\sum_{n=1}^{\infty} 2^{-n} = 1\). Aynı toplam gösterimde: \[ \sum_{n=1}^{\infty} 2^{-n} = 1 \] Metin içinde çarpım \(\prod_{i=a}^{b} f(i)\). Aynı çarpım gösterimde: \[ \prod_{i=a}^{b} f(i) \] \section{Limitler} Metin içinde limit \(\lim_{x\to\infty} f(x)\). Aynı limit gösterimde: \[ \lim_{x\to\infty} f(x) \] \end{document} ``` [Bu örneği Overleaf'te açın](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) ## Daha fazla okuma Daha fazla bilgi için bakınız * [Matematiksel ifadeler](/latex/tr/matematik/01-mathematical-expressions.md) * [Alt ve üst simgeler](/latex/tr/matematik/02-subscripts-and-superscripts.md) * [Kesirler ve Binomlar](/latex/tr/matematik/05-fractions-and-binomials.md) * [Matematik modunda gösterim stili](/latex/tr/matematik/10-display-style-in-math-mode.md) --- # Agent Instructions This documentation is published with GitBook. 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