Antiderivative-practice-basics.tex

\Section{Antiderivative practice---basics}

Find the following antiderivatives.

\begin{multicols}{2}
 \begin{ProblemSet}[pencil space=3.75in]
  \EqProb{F(x) = \IndefiniteIntegral{x^5}{x}}
  \EqProb{G(x) = \IndefiniteIntegral{8 x^5}{x}}
  \EqProb{H(p) = \IndefiniteIntegral{\left( 8 p^5 + 6 p^4 + 3 p - 6\right)}{p}}
  \EqProb{M(w) = \IndefiniteIntegral{w^{\nicefrac{1}{3}}}{w}}
  \EqProb{K(t) = \IndefiniteIntegral{\frac{10}{t}}{t}}
  \EqProb{P(z) = \IndefiniteIntegral{\frac{10}{3z}}{z}}
  \EqProb{F(x) = \IndefiniteIntegral{\left(5 x\right)^2}{x}}
  \EqProb{G(x) = \IndefiniteIntegral{\left(5 + x\right)^2}{x}}
 \end{ProblemSet}
\end{multicols}

\begin{ProblemSet}[pencil space=2in]
 \begin{Problem}
  Find the function $F(x)$ with the properties that
  \begin{itemize}
  \item $F'(x) = 5 x^2$
  \item $F(0) = 10$
  \end{itemize}
 \end{Problem}
 \begin{Problem}
  Find the function $G(x)$ with the properties that
  \begin{itemize}
  \item $G'(x) = 3 x - x^2$
  \item $G(4) = 1$
  \end{itemize}
 \end{Problem}
 \begin{Problem}
  Find a degree-three polynomial that has a local minimum at the point $(0, -4)$ and a local maximum at the point $(2, 2)$.
 \end{Problem}
\end{ProblemSet}

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