Integration: Applications
https://maa.org/taxonomy/term/40469/all
enWaiting to Turn Left?
https://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>Suspension Bridge Profiles
https://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"><p><em>The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.</em></p>
</div></div></div>The Average Distance of the Earth from the Sun
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-average-distance-of-the-earth-from-the-sun
<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>Find the averages of the distances with respect to different variables.</i></p>
</div></div></div>Euler's Other Proof
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/eulers-other-proof
<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>This is a short proof of a famous result of Euler about summation of the following series: \(\sum 1/{n^2} = {\pi^2}/6\).</em></p>
</div></div></div>The Alternating Harmonic Series
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-alternating-harmonic-series
<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 provides an elementary proof that the alternating harmonic series converges to \(\ln 2\).</em.></div></div></div>Inequalities of the Form \( f(g(x)) \geq f(x)\)
https://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>On the Work to Fill a Water Tank
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-work-to-fill-a-water-tank
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>This article describes an alternate way to motivate the integral set up for work done in raising water in a tank.</em></div></div></div>Finding Curves with Computable Arc Length
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finding-curves-with-computable-arc-length
<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 describes a method for identifying curves where the arc length is easy to compute by symbolic integration.</em></p>
</div></div></div>A Dozen Minima for a Parabola
https://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>Arc Length and Pythagorean Triples
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/arc-length-and-pythagorean-triples
<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>A family of curves whose lengths are closely related to Pythagorean Triples and therefore rational</em></p>
</div></div></div>A Simple Introduction to \(e\)
https://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
https://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>Characterizing Power Functions by Volumes of Revolution
https://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>The Buckled Rail: Three Formulations
https://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
https://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>