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# The Gateway Arch in St. Louis (see the photo on page 543) was constructed using the equation$$y = 211.49 - 20.96 \cosh 0.03291765x$$for the central curve of the arch, where $x$ and $y$ are measured in meters and $\mid x \mid \le 91.20$.Set up an integral for the length of the arch and use your calculator to estimate the length correct to the nearest meter.

## 451 meter

#### Topics

Applications of Integration

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### Video Transcript

it's clear. So when you right here. So we have. Why is equal to 200 11.49 minus 20 0.96 kash of Sarah 0.0 3 to 9. 1765 Next, the absolute value of X is less than or equal to 91 point two. So we're gonna find for the derivative. We got negative 20 Wait 96 Time 0.3 29 1765 The hyperbolic function of sign 0.3 to 9. 17 65 Thanks. So, using the art link formula, we go from negative 91.2 to positive 91.2 the square root of one plus negative. 20.96 Time 0.32 91765 My public function of sign the 0.3 to 9 1765 x and we're going to square this indeed X. This is equal to or injured 51.135 into the nearest meter. It becomes 451 meters, huh?

#### Topics

Applications of Integration

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