Integration: Applications
http://www.maa.org/taxonomy/term/40469/0
enInequalities of the Form \( f(g(x)) \geq f(x)\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/inequalities-of-the-form-fgx-geq-fx
<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 author gives two applications of a method for finding a function \(g\) such that \(f(g(x)) \geq f(x)\).</em></p>
</div></div></div>Suspension Bridge Profiles
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/suspension-bridge-profiles
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.</em></div></div></div>Waiting to Turn Left?
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/waiting-to-turn-left
<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 authors model a real traffic problem by using the fundamental theorem of calculus.</em></p>
</div></div></div>Characterizing Power Functions by Volumes of Revolution
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/characterizing-power-functions-by-volumes-of-revolution
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The authors characterize power functions by ratios of two specific volumes.</em></div></div></div>A Simple Introduction to \(e\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-simple-introduction-to-e
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Look for a number \(e\) between \(2\) and \(3\) for which the area under \(y=1/x\) from \(1\) to \(e\) is \(1\).</em></div></div></div>An Improved Remainder Estimate for Use with the Integral Test
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-improved-remainder-estimate-for-use-with-the-integral-test
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>If a series is shown convergent by the integral test, get a sharper than usual estimate for the error.</em></div></div></div>Hyperbolic Functions and Proper Time in Relativity
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/hyperbolic-functions-and-proper-time-in-relativity
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Links hyperbolic functions to distance measurement in space-time</i></p>
</div></div></div>The Buckled Rail: Three Formulations
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-buckled-rail-three-formulations
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Computing heights of three shapes of buckled rail</i></p>
</div></div></div>A Bug Problem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-bug-problem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A bug is on the inside of a container that has the shape of a paraboloid \(y=x^2\) revolved about the \(y\)-axis. If a liquid is poured into the container at a constant rate, how fast does the bug have to crawl to stay dry?</em></div></div></div>Symmetry at Infinity
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/symmetry-at-infinity
<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 centroid of the region bounded by \(y=x^n\) and \(y=x^{1/n}\) is not the same for all \(n\).</em></p>
</div></div></div>Self-integrating Polynomials
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/self-integrating-polynomials
<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>Student error leads author to seek polynomials for which \(p(1)-p(0)\) equals the integral of \(p(x)\) on \([0,1]\).</em></p>
</div></div></div>How Do You Slice the Bread?
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/how-do-you-slice-the-bread
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>How do you cut a slice of bread (rectangle surmounted by an ellipse) into two "triangles" to equalize the areas?</i></p>
</div></div></div>Can You Paint a Can of Paint?
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/can-you-paint-a-can-of-paint
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Author tries to resolve the paradox of the paint can that can be filled, but not covered with paint.</i></p>
</div></div></div>A Paradoxical Paint Pail
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-paradoxical-paint-pail
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>A new can, this one bounded, again has the property of having a finite volume, but an infinite surface area.</i></p>
</div></div></div>A Dozen Minima for a Parabola
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-dozen-minima-for-a-parabola
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Except at the vertex, the normal to a parabola at \(P\) intersects it again at a point \(Q\). There are many interesting minimization problems generated by the line segment \(PQ\).</em></div></div></div>