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\centerline{MATH 136 -- Calculus 2}
\centerline{Practice Day on Trigonometric Integrals}
\centerline{February 11, 2020}
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\noindent
{\it Background}
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Our approach to trigonometric integrals will be based in systematic
application of \emph{reduction formulas} like the ones we saw yesterday.  
When you do these 
and exams, the formulas on the sheet I distributed \emph{will be provided} for your
use in table format.  You will be responsible for deciding which formula
applies and for applying it correctly.  Here are some practice problems.
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\noindent
{\it Questions}
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For each of the following integrals, decide which of the reduction formula applies,
determine the appropriate $n$ (and $m$ in the last two).  Then apply the formula and
complete the computation.
\begin{enumerate}
\item $\displaystyle \int \sin^2(x)\ dx$
\item $\displaystyle \int \sec^3(x)\ dx$
\item $\displaystyle \int \cos^4(3x)\ dx$
\item $\displaystyle \int \tan^2(4x) \sec^3(4x)\ dx$ (Use $\tan^2(u) = 1 + \sec^2(u)$, then ST3.)
\item $\displaystyle \int \tan^3(5x)\sec^5(5x)\ dx$ (Convert to powers of $\sin(u)$ and $\cos(u)$.) 

\end{enumerate}
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\caption{The region for problem 4.}
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