James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

8
Further Applications of
Integration
The Gateway Arch in St. Louis,
Missouri, stands 630 feet
high and was completed in
1965. The arch was designed
by Eero Saarinen using
an equation involving the
hyperbolic cosine function.
In Exercise 8.1.42 you are
asked to compute the length
of the curve that he used.
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We looked at some applications of integrals in Chapter 6: areas, volumes, work, and average
values. Here we explore some of the many other geometric applications of integration — the
length of a curve, the area of a surface —as well as quantities of interest in physics, engineering,
biology, economics, and statistics. For instance, we will investigate the center of gravity of a
plate, the force exerted by water pressure on a dam, the flow of blood from the human heart, and
the average time spent on hold during a customer support telephone call.
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