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# The Gateway Arch in St. Louis (see the photo on page 583) was constructed using the equation y = 211.49 − 20.96 cosh 0 .03291765 x for the central curve of the arch, where x and y are measured in meters and | x | ≤ 91.20 . Set up an integral for the length of the arch and use your calculator to estimate the length correct to the nearest meter.

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### Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

#### Solutions

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Section
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### Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
Chapter 8.1, Problem 42E
Textbook Problem
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## The Gateway Arch in St. Louis (see the photo on page 583) was constructed using the equation y = 211.49 − 20.96   cosh  0 .03291765 x for the central curve of the arch, where x and y are measured in meters and | x | ≤ 91.20 . Set up an integral for the length of the arch and use your calculator to estimate the length correct to the nearest meter.

To determine

To estimate:

The length of the arc correct to the nearest meter.

### Explanation of Solution

1) Concept:

Use the arc length formula to find the length of the arc.

2) Formula:

If f' is continuous on a,b,  then the length of the curve  y=fx, axb,   is

L=ab1+f'x2dx=ab1+dydx2dx

3) Given:

y=211.49-20.96cosh0.03291765·x,  x91.20

4) Calculation:

Let,

fx=y=211.49-20.96cosh0.03291765·x

And x91.20, that is

-91.20x91.20

Differentiate   y=f(x) with respect to   x

dydx=0-20.96·0.03291765·sinh0.03291765·x

dydx=-0.097936244sinh0

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