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\title{How long is a parabola?}
\date{September 30, 2020}

\begin{document}

\ \vspace{-.25in}

\maketitle

\vspace{-.15in}

\prob{ The goal of this worksheet is to determine the arc length of a segment of the parabola $y=x^2$.

\begin{enumerate}[a)]

\item Set up an integral giving the arc length of $y=x^2$ from $0$ to $1$. For now we'll ignore the limits of integration, so you can leave them off for steps b through e.

\item Make a trigonometric substitution to convert to a trig integral.

\item Use integration by parts.

\item Use a trig identity to cycle back to the starting trig integral and then solve for the integral (like problem 1 of the last worksheet).

\item Convert back to x using a triangle.

\item Now use the original limits of integration and evaluate the integral to find the arc length.

\end{enumerate}
}

\chal{
Find an arc length function $s(x)$ for the parabola $y=x^2$.
}

\chal{
Verify that your antiderivative for $\sqrt{1 + 4x^2}$ is correct.
}

\end{document}