練習問題にチャレンジ♪
さっそく練習問題にチャレンジしましょう。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{2} \def\SekibunS{1} \def\Kotae{x} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK \,\colFR{orange}{$dx$} &= \dfrac{\MondaiK x^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{1} \def\SekibunS{2} \def\Kotae{\dfrac12x^2} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK x^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dx$} &= \dfrac{\MondaiK x^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{2} \def\SekibunS{3} \def\Kotae{\dfrac13x^3} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK x^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dx$} &= \dfrac{\MondaiK x^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{4} \def\MondaiS{2} \def\SekibunS{3} \def\Kotae{\dfrac43x^3} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK x^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dx$} &= \dfrac{\MondaiK x^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{6} \def\MondaiS{2} \def\SekibunS{3} \def\Kotae{2x^3} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK x^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dx$} &= \dfrac{\MondaiK x^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{2} \def\SekibunS{1} \def\Kotae{t} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow t} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK \,\colFR{orange}{$dt$} &= \dfrac{\MondaiK\ t^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{1} \def\SekibunS{2} \def\Kotae{\dfrac12u^2} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow u} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK u^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$du$} &= \dfrac{\MondaiK u^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{2} \def\SekibunS{3} \def\Kotae{\dfrac13y^3} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow y} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK y^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dy$} &= \dfrac{\MondaiK y^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\MondaiK{1} \def\MondaiS{2} \def\SekibunS{3} \def\Kotae{\dfrac13y^3} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow y} & \colMM{orange}{を増やす\downarrow} \colMM{red}{\Darr 積分定数を忘れずに}\\ \int \MondaiK y^{\colBX{bisque}{$\scriptsize \MondaiS$}}\,\colFR{orange}{$dy$} &= \dfrac{\MondaiK y^{\colBX{bisque}{$\scriptsize \SekibunS$}}}{\colBX{palegreen}{$\small\SekibunS$}}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \Kotae\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{orange}{\nearrow x} & \colMM{orange}{を増やす\downarrow} \colMM{red}{積分定数 \Darr を忘れずに}\\ \int (-1x^{\colBX{bisque}{$\scriptsize 2$}}+3x^1) \,\colFR{orange}{$dx$} &= \dfrac{-1x^{\colBX{bisque}{$\scriptsize 3$}}}{\colBX{palegreen}{$\small 3$}}+\dfrac{3 x^{2}}{2}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= -\dfrac13x^3+\dfrac32x^2\ +\ C \end{align*}
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & \int (x+4)(x-2)\,dx\\ & \colMM{red}{\Darr まずは展開してから}\\ &= \int (1x^{\colBX{bisque}{$\scriptsize 2$}}+2x^1-8\textcolor{lightgray}{x^0}) \,\colFR{orange}{$dx$}\\ & \colMM{orange}{\downarrow xを増やす} \colMM{red}{積分定数 \Darr を忘れずに}\\ &= \dfrac{1x^{\colBX{bisque}{$\scriptsize 3$}}}{\colBX{palegreen}{$\small 3$}}+\dfrac{2 x^{2}}{2}-\dfrac{8 x^{1}}{1}\ \colBX{mistyrose}{$+\ C$}\\ & \colMM{green}{\nwarrow 割る}\\ &= \dfrac13x^3+x^2-8x\ +\ C \end{align*}