この問題には解答がありません。作成中ですのでしばらくお待ちください。
入試情報
大学名 |
京都府立医科大学 |
学科・方式 |
前期 |
年度 |
2006年度 |
問No |
問4 |
学部 |
医学部
|
カテゴリ |
積分法
|
状態 |
 |
%
% すうじあむはアップするファイルで完結したTeXソースでないといけない.
% このひな形で表示確認をしよう.
%
\documentclass[b5paper,fleqn,papersize]{jsarticle}
%===========================================================
% ■余白の設定 B5
%-----------------------------------------------------------
\setlength{\oddsidemargin}{-5.4truemm} % 左マージン
\setlength{\topmargin}{-15.4truemm} % 上マージン
\setlength{\textwidth}{14.2cm} % B5 サイズ用
\setlength{\headheight}{2zw}
\setlength{\headsep}{2zw}
\setlength{\textheight}{217mm}
%===========================================================
\usepackage[dvipdfm]{graphicx}
\usepackage{wrapfig}
% \usepackage{amsmath,amsthm,amssymb,cases}
\usepackage{amsmath,amsthm,amssymb}% すうじあむはcasesが使えない?
\usepackage{multicol}
\usepackage{ascmac}
\usepackage{fancybox}
\usepackage{framed}
\usepackage{ifthen}
\usepackage{setspace} % setspaceパッケージのインクルード
\usepackage{amssymb}% ≒を表示するために必要
\usepackage{comment}% コメント
\usepackage{booktabs}
\usepackage{ascmac}
% \usebackage{eclbkbox}% すうじあむはこれもダメ
\usepackage{itembbox}
%
% \usepackage{ custom_suseum}% すうじあむ
%=========================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% enumerate の自動ラベルの変更
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\labelenumi{(\theenumi)}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 増減表の矢印
% http://www.biwako.shiga-u.ac.jp/sensei/kumazawa/tex/arrow.html
%
% $\cvinc$ increase
% $\ccinc$ concavity 凹状の
% $\cvdec$ convex 凸形の
% $\ccdec$ decrease
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
\newcommand{\ccinc}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(1,2)
\put(1,2){\line(0,1){3}}
\put(5,5){\oval(8,8)[lt]}
\put(5,9){\vector(1,0){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(1,2)
\put(1,2){\line(0,1){3}}
\put(5,5){\oval(8,8)[lt]}
\put(5,9){\vector(1,0){4}}
\end{picture}\fi}
\newcommand{\cvinc}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(2,1)
\put(2,1){\line(1,0){3}}
\put(5,5){\oval(8,8)[rb]}
\put(9,5){\vector(0,1){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(2,1)
\put(2,1){\line(1,0){3}}
\put(5,5){\oval(8,8)[rb]}
\put(9,5){\vector(0,1){4}}
\end{picture}\fi}
\newcommand{\ccdec}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(2,1)
\put(2,9){\line(1,0){3}}
\put(5,5){\oval(8,8)[rt]}
\put(9,5){\vector(0,-1){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(2,1)
\put(2,9){\line(1,0){3}}
\put(5,5){\oval(8,8)[rt]}
\put(9,5){\vector(0,-1){4}}
\end{picture}\fi}
\newcommand{\cvdec}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(1,0)
\put(1,8){\line(0,-1){3}}
\put(5,5){\oval(8,8)[lb]}
\put(5,1){\vector(1,0){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(1,0)
\put(1,8){\line(0,-1){3}}
\put(5,5){\oval(8,8)[lb]}
\put(5,1){\vector(1,0){4}}
\end{picture}\fi}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%======================================================================
\newcommand{\解説}{\noindent\ovalbox{\bf 解説}\hspace{0.5em}}
\newcommand{\解答}{\noindent\fbox{\bf 解答}\hspace{0.5em}}
\newcommand{\別解}{\noindent\fbox{\bf 別解}\hspace{0.5em}}
%======================================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%■ベクトルの矢印の高さを揃える定義
% \overrightarrow の矢印の高さを揃える
% \vec, \Vec で定義する
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\vec#1{\overrightarrow{\mathstrut #1}}
\def\Vec#1{\overrightarrow{\mathstrut {\rm #1}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%===========================================================
% ■二重根号
%-----------------------------------------------------------
\def\tsqrt#1{\textstyle\sqrt{#1}}
%===========================================================
%%% 平行 // の記号%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\para{%
\setlength{\unitlength}{1pt}%
\thinlines %
\begin{picture}(10, 12)%
\put(1,0){/}%
\put(4,0){/}%
\end{picture}%
}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%■ 答えを太文字
\newcommand{\kotae}[1]{\mbox{\boldmath$#1$}}
% \def\kotae#1{\mbox{\boldmath $#1$}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%===========================================================
% ■枠囲み
%-----------------------------------------------------------
\newcommand{\枠囲}[1]{\,\fboxsep1pt\fbox{ #1 }\,}% 文章中でも数式中でも使える?
% \newcommand{\枠}[1]{\fboxsep1pt\fbox{ #1 }\,}
%===========================================================
%===========================================================
% ■≦と≧の定義
%-----------------------------------------------------------
\def\le{\leqq}
\def\ge{\geqq}
\newcommand{\LEQQ}{\leqq}
\newcommand{\GEQQ}{\geqq}
% \newcommand{\LEQQ}{\mathrel{\mathpalette\gl@align<}}
% \newcommand{\GEQQ}{\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}}}
% エラーになる。理由はよく解らん。
%===========================================================
%===========================================================
% ■行列 2×2
%-----------------------------------------------------------
\newcommand{\matrixTT}[4]{
\begin{pmatrix}
#1 & #2 \\
#3 & #4
\end{pmatrix}
}
%===========================================================
%===========================================================
% ■行列 3×3
%-----------------------------------------------------------
\newcommand{\matrixTTT}[9]{
\begin{pmatrix}
#1 & #2 & #3\\
#4 & #5 & #6\\
#7 & #8 & #9
\end{pmatrix}
}
%===========================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ■ 3*1行列の定義
\newcommand{\matrixthreeone}[3]{
\left(\begin{array}{c}
#1\\
#2\\
#3
\end{array}\right)
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%===========================================================
% ■角括弧 複数行 #1 は横幅%,#2は内容
%
%-----------------------------------------------------------
\newcommand{\角括弧}[2]{%
$%
\left[ \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right]%
$%
}
%===========================================================
%===========================================================
% ■丸括弧 複数行 #1 は横幅%,#2は内容
%-----------------------------------------------------------
\newcommand{\丸括弧}[2]{%
$%
\left( \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right)%
$%
}
%===========================================================
%===========================================================
% ■丸囲み数字 ①とか
%-----------------------------------------------------------
\newcommand{\tyoMaru}[1]{\mbox{{\normalsize \textcircled{\scriptsize #1}}}}
%===========================================================
%===========================================================
% ■ 微分 df/dt
%-----------------------------------------------------------
\newcommand{\dd}[2]{%
\dfrac{{\rm d}#1}{{\rm d}#2}%
}
%===========================================================
%===========================================================
% ■ ∫記号のdisplaystyleマクロ
%-----------------------------------------------------------
% \newcommand{\dint}{\displaystyle\int}% emathと干渉しないように\defで定義
\def\dint{\displaystyle\int}
%===========================================================
%===========================================================
% ■ Σ記号のdisplaystyleマクロ
%-----------------------------------------------------------
\newcommand{\dsum}{\displaystyle\sum}
%===========================================================
%===========================================================
% ■ lim記号のdisplaystyleマクロ
%-----------------------------------------------------------
\newcommand{\dlim}{\displaystyle\lim}
%===========================================================
%===========================================================
% ■ nCr マクロ
%-----------------------------------------------------------
\newcommand{\nCr}[2]{%
{}_{#1}\mathrm{C}_{#2}%
}
%===========================================================
%===========================================================
% ■ 証明終了記号 ■
%-----------------------------------------------------------
\newcommand{\■}{{\tiny \text{■}}}
%===========================================================
\begin{document}
%%%%% ■ 本文開始 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{FRAME}% この間に設問を書く
\begin{enumerate}
\item 関数$f(x)$はすべての実数で定義されていて,連続な第2次導関数$f''(x)$をもつとする.このとき,
\[\dint_0^x\{f(t)+f''(t)\}\sin{t}\, dt=f(0)-f(x)\cos{x}+f'(x)\sin{x}\]
が成り立つことを示せ.
\item 不定積分$\dint xe^x\sin{x}\, dx$を求めよ.
\end{enumerate}
% \end{FRAME}
%--- 解答 ------------------------------------------------------------------------
%%%%%%% ■ 本文終了 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}