An overhead utility cable is suspended along the graph of between the vertical poles…

MATHEMATICS · Multi-part · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

An overhead utility cable is suspended along the graph of

y=\ln|\sec x|

between the vertical poles located at

x=0

and

x=\dfrac{\pi}{4}

. Horizontal distance

x

is measured in metres, and

y

is measured in metres above ground level. (a) Compute

\dfrac{dy}{dx}

and simplify your result. (b) Determine the exact length of cable required between the two poles by evaluating the appropriate definite integral. Show complete justification for each step of your work. (c) Explain how the functional form of

y

guarantees that the cable length found in part (b) exceeds the straight‐line distance between the poles.

Related theory

Advanced Differentiation
Advanced Applications
Derivatives of standard functions via chain rule
Exponential and logarithmic functions
Continuity and Differentiability
Implicit and Parametric Differentiation
Applications of Integration

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