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\noindent {\LARGE M}{\large ath} {\LARGE 120} {\LARGE S}{\large pring} {\LARGE 98}
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{\Large Quiz {\bf 5}}\hspace{7cm} & \hspace{1.65in} & \\
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Name: \makebox[2in]{\hrulefill}  & \hspace{1.5in} & \\
 & \hspace{1.5in} &  Basic~Calculus~2  \\
Date: \makebox[2in]{\hrulefill} & \hspace{1.5in} & {\bf Wednesday March 4, 1998} \\
Time Begun: \makebox[2in]{\hrulefill} & \hspace{1.5in} & Ron Buckmire \\ 
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{\Large {\bf Topic covered:}} Integration by Substitution or Parts

{\small The point of this quiz is to give you more practice with using the methods of integration by substitution and integration by parts to evaluate integrals.}

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{\Large {\bf Instructions: }}
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\item[1.] Once you open the quiz, you have 60 minutes to complete it.
\item[2.] You may use the book or any of your class notes, and you may use a calculator.  You must work alone.
\item[3.] If you use your own paper, please staple it to the quiz before coming to class.  If you don't have a stapler, buy one.
\item[4.] After completing the quiz, sign the pledge below stating on your honor that you have adhered to these rules.  
\item[5.] Relax and enjoy...
\item[6.] {\bf This quiz is due on Monday, March 9}, in class.  NO LATE QUIZZES WILL BE ACCEPTED.
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{\bf Pledge:} I, \makebox[2in]{\hrulefill}, pledge my honor as a human being and Occidental student, that I have followed all the rules above to the letter and in spirit.
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Math 120 Spring 1998 \hfill{Quiz {\bf 5}}
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\vspace{-7.5ex}   {\large\bf SHOW ALL YOUR WORK}\\
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Two students are discussing different approaches to evaluating a particular integral, $I = {\boldmath \displaystyle \int_1^2 e^{\sqrt{x}} dx }$
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\item[Devon:] Clearly there is no way to evaluate this integral.
\item[Lee:] But this is a definite integral, so we must be able to apply the Fundamental Theorem of Calculus to obtain a value for it (it's just a number).
\item[Devon:] Hmmm, well now that you mention that it's a definite integral I remembered that we can estimate any definite integral using Riemann sums like Simpson's Rule.
\item[Lee:] Why bother? We can use integration by substitution and let $u=\sqrt{x}$, therefore $du = \frac{dx}{2 \sqrt{x}}$ and we can rewrite the given integral as ${\displaystyle \int_1^{\sqrt{2}} 2 u e^u du}$ and then integrate by parts and get an approximate answer.
\item[Devon:] Well, you have to do all that work to get an approximate answer and I can just plug some symbols into a {\tt TruBasic} program and also get an estimate, so I think my way is better!
\end{itemize}
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}
{\bf [1.]} ({\it 10 points}) Write a couple of paragraphs discussing the students' understanding of Calculus. Identify {\bf any} and all correct or incorrect statements made by the students. If a statement is incorrect explain why. {\bf You must be careful not to make any incorrect statements yourself in your explanation.} PROOFREAD YOUR ANSWER.
 
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