%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{calc,patterns}
%\usetikzlibrary{arrows.meta,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\def\maruwaku#1{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=3mm,text margin right=3mm}
\fboxrule=0.8pt

\makeatletter
\def\hooklen#1#2{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=0pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu%■default
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
%\medmuskip=4mu plus 2mu minus 4mu%■default
\medmuskip=1mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu%■default
% mu は math units の省略で長さの単位

\newcommand{\maru}{\text{\textcolor{CUDRed}{●}}}
\newcommand{\sankaku}{\text{\textcolor{CUDBlue}{▲}}}

%■ 新しいプラスマイナス記号を自作（TikZを利用）
\newcommand{\newpm}{\,\tikz[baseline=-0.1ex]
	\draw[line width=0.1ex,line cap=round](0,0)--++(0.6em,0)
					(0,0.8ex)--++(0.6em,0)
					(0.3em,0.25ex)--++(0,1.1ex);
	\,}
\newcommand{\ittan}{\begin{tikzpicture}[scale=0.7,
	baseline={([yshift=-21pt] current bounding box.north)}]
\filldraw[very thick,draw=CUDBlue,fill=CUDYellow,rounded corners=1pt]
	(0,0)--++(0.8,0)--++(0,0.8)--++(-0.8,0)--cycle;
\draw(0.4,0.4) node[CUDBlue]
	{\fontsize{7pt}{7pt}\selectfont
		\shortstack{一旦\\[-2pt]停止}};
\end{tikzpicture}
}

%■■■■■■■■■■■　実験エリア　■■■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■　ここから本文　■■■■■■■■■■■■■■■■


\begin{frame}[t]
\frametitle{定積分\qquad\(6\)分の\(1\)公式}
\centerline{%
\begin{beamercolorbox}[wd=0.9\textwidth,ht=4ex,dp=2.4ex,shadow=true,
	rounded=true, center]{CUDCream}
\( \int_\maru^\sankaku \kern-0.5em(x-\maru)(x-\sankaku) \,dx
	 = -\,\myfrac{\,1\,}{6}\,(\sankaku-\maru)^3 \)
\end{beamercolorbox}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(1\)}
\vskip-5ex
\begin{eqnarray*}
\int_{-1}^{3} \kern-0.5em (x+1)(x-3) \,dx
	&=& \kern-0.5em\int_{\textcolor{CUDRed}{-1}}^{\textcolor{CUDBlue}{3}}
	\kern-0.3em \Bigl(x-\textcolor{CUDRed}{(-1)}\Bigr)
		(x-\textcolor{CUDBlue}{3}) \,dx \\
	&=& -\,\myfrac{\,1\,}{6}\,\Bigl(\textcolor{CUDBlue}{3}
		-\textcolor{CUDRed}{(-1)}\Bigr)^3 \\
	&=& -\,\myfrac{\,1\,}{6}\cdot\quad 4^3 \\
	&=& -\,\myfrac{\,32\,}{3}\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(2\)}
\vskip-4.4ex
\begin{eqnarray*}
\int_{-3}^{2} (x^2+x-6) \,dx
	&=& \kern-0.5em\int_{-3}^{2} (x+3)(x-2) \,dx \\
	&=& \kern-0.5em\int_{\textcolor{CUDRed}{-3}}^{\textcolor{CUDBlue}{2}}
	\kern-0.3em \Bigl(x-\textcolor{CUDRed}{(-3)}\Bigr)
		(x-\textcolor{CUDBlue}{2}) \,dx \\
	&=& -\,\myfrac{\,1\,}{6}\,\Bigl(\textcolor{CUDBlue}{2}
		-\textcolor{CUDRed}{(-3)}\Bigr)^3 \\
	&=& -\,\myfrac{\,1\,}{6}\cdot 5^3
		\quad = -\,\myfrac{\,125\,}{6}\ \text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(3\)}
\( \int_{-1}^{\frac{\,1\,}{2}} (2x^2+x-1) \,dx \)\quad を求めなさい。

\vskip-2ex
\begin{eqnarray*}
\hooklen{(2x-1)(x+1)}{2x^2+x-1} &=& 0 \quad\text{とおくと}\\
(2x-1)(x+1)&=&0 \\
x=\myfrac{\,1\,}{2},-1 \quad & & \hspace*{-2em}\text{なので}
\end{eqnarray*}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(3\)}
\vskip-4.4ex
\begin{eqnarray*}
& & \hspace*{-4em}\int_{-1}^{\frac{\,1\,}{2}} (2x^2+x-1) \,dx \\
	&=& \int_{-1}^{\frac{\,1\,}{2}}
		\textcolor{CUDGreen}{2}\,(x+1)
		\Bigl(x-\myfrac{\,1\,}{2}\Bigr) \,dx \\
	&=& \textcolor{CUDGreen}{2} \int_{\textcolor{CUDRed}{-1}}
		^{\textcolor{CUDBlue}{\frac{\,1\,}{2}}}
		\Bigl(x-\textcolor{CUDRed}{(-1)}\Bigr)
		\Bigl(x-\textcolor{CUDBlue}{\myfrac{\,1\,}{2}}\Bigr) \,dx
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(3\)}
\vskip-4.4ex
\begin{eqnarray*}
	&=& \textcolor{CUDGreen}{2} \int_{\textcolor{CUDRed}{-1}}
		^{\textcolor{CUDBlue}{\frac{\,1\,}{2}}}
		\Bigl(x-\textcolor{CUDRed}{(-1)}\Bigr)
		\Bigl(x-\textcolor{CUDBlue}{\myfrac{\,1\,}{2}}\Bigr) \,dx 
				\\[1ex]
	&=& \textcolor{CUDGreen}{2}\cdot
		-\,\myfrac{\,1\,}{6}\,\Bigl(
		\textcolor{CUDBlue}{\myfrac{\,1\,}{2}}
		-\textcolor{CUDRed}{(-1)}\Bigr)^3 \\[1ex]
	&=& \quad -\,\myfrac{\,1\,}{3}\Bigl(\myfrac{\,3\,}{2}\Bigr)^3
		\quad = -\,\myfrac{\,9\,}{8}\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(4\)}
\vskip-1ex
\( \int_{2-\sqrt{3}}^{2+\sqrt{3}} (x^2-4x+1) \,dx \)\quad を求めなさい。

\bigskip
\( x^2-4x+1=0 \)\quad とおいて、解の公式で解く。

\vskip-2ex
\begin{eqnarray*}
x &=& \myfrac{-(-4)\newpm\sqrt{(-4)^2-4\cdot1\cdot1}}{2\cdot1} \\
 &=& \myfrac{4\newpm\sqrt{12}}{2} \ =\myfrac{4\newpm2\sqrt{3}}{2}
	\ =2\newpm\sqrt{3}\ \ittan
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(4\)}
\vskip-4.4ex
\begin{eqnarray*}
& & \hspace*{-2em}\text{だから}\ 
	\int_{2-\sqrt{3}}^{2+\sqrt{3}} (x^2-4x+1)  \,dx \\
	&=& \int_{\textcolor{CUDRed}{2-\sqrt{3}}}
		^{\textcolor{CUDBlue}{2+\sqrt{3}}}
		\Bigl(x-\textcolor{CUDRed}{(2-\sqrt{3})}\Bigr)
		\Bigl(x-\textcolor{CUDBlue}{(2+\sqrt{3})}\Bigr) \,dx \\[1ex]
	&=& -\,\myfrac{\,1\,}{6}\,
		\Bigl(\textcolor{CUDBlue}{(2+\sqrt{3})}
		-\textcolor{CUDRed}{(2-\sqrt{3})}\Bigr)^3
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(6\)分の\(1\)公式\quad 例題\(4\)}
\vskip-4.4ex
\begin{eqnarray*}
	&=& -\,\myfrac{\,1\,}{6}\,
		\Bigl(\textcolor{CUDBlue}{(2+\sqrt{3})}
		-\textcolor{CUDRed}{(2-\sqrt{3})}\Bigr)^3 \\
	&=& -\,\myfrac{\,1\,}{6}\,\bigl(2\sqrt{3}\bigr)^3 \\
	&=& -\,\myfrac{\,1\,}{6}\cdot 2^3 \cdot\bigl(\sqrt{3}\bigr)^3 \\
	&=& -\,\myfrac{\,1\,}{6}\cdot\hooklen{2^3}{8} \cdot 3\sqrt{3}
	\quad =-4\sqrt{3}\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





\end{document}

