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author | syn <isaqtm@gmail.com> | 2020-04-15 04:35:30 +0300 |
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committer | syn <isaqtm@gmail.com> | 2020-04-15 04:35:30 +0300 |
commit | f642380d55c66e4e5deaaa6c7cef15f6dbfe36c6 (patch) | |
tree | 31ed9377de27678b376668131e0cbf8a8639ce16 /sol0210.tex | |
parent | 406cd62e6c18587b2859bf77434527f2ac87027d (diff) | |
download | tex2-f642380d55c66e4e5deaaa6c7cef15f6dbfe36c6.tar.gz |
Reorganize & alg-1
Diffstat (limited to 'sol0210.tex')
-rw-r--r-- | sol0210.tex | 56 |
1 files changed, 0 insertions, 56 deletions
diff --git a/sol0210.tex b/sol0210.tex deleted file mode 100644 index bb4ad94..0000000 --- a/sol0210.tex +++ /dev/null @@ -1,56 +0,0 @@ -\documentclass[10pt,a5paper]{article} -\usepackage[svgnames, rgb]{xcolor} - -\input{intro} - -\lhead{\color{gray} Шарафатдинов Камиль 192} -\rhead{\color{gray} \texttt{sol0203}} -\title{ДЗ на 10.02} -\author{Шарафатдинов Камиль БПМИ-192} -\date{билд: \today} - - -% -- Here bet dragons -- -\begin{document}\thispagestyle{empty} - -\maketitle -\clearpage -\setcounter{page}{1} - -\question{1.f}{ - \[ - \int_1^e \sin \log x \dif x - \] -} - - \begingroup - \setlength{\jot}{8pt} - \begin{align*} - I = \int \sin \log \dif x - &= \int e^u \sin u \dif u - &\explain{ - \displaystyle u = \log x\\ - \displaystyle \dif u = \frac{\dif x}{x} = \frac{\dif x}{e^u} - }\\ - &= - e^u \cos u + \int e^u \cos u \dif u\\ - &= - e^u \cos u + e^u \sin u - \int e^u \sin u \dif u - \end{align*} - \endgroup - - \begin{flalign*} - 2I = e^u (\sin u - \cos u) + C\\ - I = \frac{e^u}{2} (\sin u - \cos u) + C = - \frac{x}{2} (\sin \log x - \cos \log x) + C - \end{flalign*} - - \[ - \int_1^e \sin \log x \dif x = - \frac{e}{2} (\sin 1 - \cos 1) - \frac{1}{2} (0 - 1) = - \frac{e}{2} (\sin 1 - \cos 1) + \frac{1}{2} - \] - -\vspace*{\fill} - - P.S. Ну проверь хотя бы одну задачу, пожаааалуйста - -\end{document} |