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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{The Fundamental Theorem of Calculus}

\begin{example}
Find an antiderivative of \[
f(x)=\sqrt{2+\sin ^{2}x}.\]

\end{example}

\subsubsection*{Real Stupid Solution}

Computationally, in terms of ordinary functions, there is no way to find this
antiderivative. There are many integration problems like this, as we'll see.
But still, there is an answer to the problem, in that \[
F(x):=\int _{0}^{x}\sqrt{2+\sin ^{2}t}dt\]
is indeed an antiderivative of \( f(x) \). This is really what the answer is
supposed to be, and it is all that anyone could say.
\end{document}
