Integration
http://www.maa.org/taxonomy/term/41616/0
enProof without Words: Integration by Parts
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-integration-by-parts
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The rule of integration by parts is proven visually.</em></p>
</div></div></div>Two Surprising Theorems on Cavalieri Congruence
http://www.maa.org/programs/maa-awards/writing-awards/two-surprising-theorems-on-cavalieri-congruence
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya</p>
<p><b>Year of Award:</b> 1992</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 22, No. 2, (1991), pp. 118-124</p>
<p><b>Summary:</b> Discusses Cavlieri's early seventeenth century work on the "method of indivisibles," and applies Cavlieri's principles to produce two unexpected results.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020746.02p00037.pdf">Read the Article</a></p></div></div></div>Inverse Problems and Torricelli's Law
http://www.maa.org/programs/maa-awards/writing-awards/inverse-problems-and-torricellis-law
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya</p>
<p><b>Year of Award:</b> 1994</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 24, No. 3, (1993), pp. 210-217</p>
<p><b>Summary:</b> Three elementary inverse problems stemming from Torricelli's law which can be used to introduce undergraduates to notions related to ill-posed problems.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020757.02p00026.pdf">Read the Article</a></p></div></div></div>Taking Limits Under the Integral Sign
http://www.maa.org/programs/maa-awards/writing-awards/taking-limits-under-the-integral-sign
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><strong>Year of Award</strong>: 1968</p>
<p class="MsoNormal"><strong>Publication Information:</strong> <em>Mathematics Magazine,</em> vol. 40, 1967, pp. 179-186</p></div></div></div>Integrals Don't Have Anything to Do with Discrete Math, Do They?
http://www.maa.org/programs/maa-awards/writing-awards/george-polya-awards/integrals-dont-have-anything-to-do-with-discrete-math-do-they
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Year of Award:</strong> 2012</p>
<p><strong>Award:</strong> Allendoerfer</p>
<p><strong>Publication Information:</strong> <em>Mathematics Magazine</em>, vol. 84, 2011, pp. 108-119</p></div></div></div>Kepler: The Volume of a Wine Barrel - Solving the Problem of Maxima: Wine Barrel Design
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-solving-the-problem-of-maxima-wine-barrel-design
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</p>
</div></div></div>Teaching the Fundamental Theorem of Calculus: A Historical Reflection
http://www.maa.org/press/periodicals/convergence/teaching-the-fundamental-theorem-of-calculus-a-historical-reflection
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">An argument that the teaching of elementary integration should better reflect its historical development</div></div></div>Teaching the Fundamental Theorem of Calculus: A Historical Reflection - Introduction
http://www.maa.org/press/periodicals/convergence/teaching-the-fundamental-theorem-of-calculus-a-historical-reflection-introduction
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">An argument that the teaching of elementary integration should better reflect its historical development</div></div></div>Teaching the Fundamental Theorem of Calculus: A Historical Reflection - Integration from Cavalieri to Darboux
http://www.maa.org/press/periodicals/convergence/teaching-the-fundamental-theorem-of-calculus-a-historical-reflection-integration-from-cavalieri-to
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">An argument that the teaching of elementary integration should better reflect its historical development</div></div></div>Teaching the Fundamental Theorem of Calculus: A Historical Reflection - Newton's Proof of the FTC
http://www.maa.org/press/periodicals/convergence/teaching-the-fundamental-theorem-of-calculus-a-historical-reflection-newtons-proof-of-the-ftc
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">An argument that the teaching of elementary integration should better reflect its historical development</div></div></div>Kepler: The Volume of a Wine Barrel - A Problem of Maxima: Wine Barrel Design
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-a-problem-of-maxima-wine-barrel-design
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Kepler: The Volume of a Wine Barrel - About the Author and Acknowledgments
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-about-the-author-and-acknowledgments
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Kepler: The Volume of a Wine Barrel - Links and References
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-links-and-references
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Kepler: The Volume of a Wine Barrel - Derivatives, Tangents, and Slopes; Conclusion
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-derivatives-tangents-and-slopes-conclusion
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</p>
</div></div></div>Average Value of a Hand-Drawn Function
http://www.maa.org/press/periodicals/loci/resources/average-value-of-a-hand-drawn-function
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">This mathlet provides an innovative tool that allows the user to sketch a function with the mouse in order to examine some common issues and misconceptions about the average value of a function.</div></div></div>