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\title{\vspace*{-1.5in}\textbf{Math 2300-007: \S5.7 - Trig Integrals }\\[1ex]\normalsize(With thanks to Faan Tone Liu)}
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\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-007: Calculus II}
\chead{January 23, 2018}
\rhead{\S5.7 - Trig integrals}
\vspace{-.5in}
\noindent
\textbf{Key points:}
\begin{itemize}
\item To integrate powers of $\sin(x)$ and $\cos(x)$ when at least one power is odd...\vskip1.2in
\item To integrate powers of $\sin(x)$ and $\cos(x)$ when at both powers are even...\vskip1.2in 
\item To integrate powers of $\sec(x)$ and $\tan(x)$...\vskip1.2in
\item Helpful Trig Identities:\vskip1.2in
\end{itemize}
Examples:
\vskip12pt
\begin{enumerate}
 \item $\displaystyle \int \sin^3x\cos^4x\,dx$ \vfill
\newpage
 \item $\displaystyle  \int_0^{\pi/4} \sin^2\theta\,d\theta$ \vfill
 \item $\displaystyle \int\sin^2\theta\cos^2\theta\,d\theta$\vfill
 \item $\displaystyle \int\tan^4x\sec^2x\,dx$\vfill
\newpage
 \item $\displaystyle \int\tan^2x\sec^4x\,dx$\vfill
 \item $\displaystyle \int\tan^3x\sec^5x\,dx$\vfill
 \item $\displaystyle \int\tan^3x\,dx$\vfill
\newpage
 \item $\displaystyle \int\tan^4x\,dx$\vfill
 \item $\displaystyle \int\sec^5x\,dx$\vfill
\end{enumerate}
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