A pedestrian walkway follows the edge of a quarter‐circle pond of radius

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

Problem

5\text{ m}

. In Cartesian coordinates the walkway is described by

y=\sqrt{25-x^{2}}

for

0\le x\le 5

, where

x

and

y

are measured in metres. (a) Formulate the definite integral that gives the length of the walkway along the pond’s edge. Express the integrand in its simplest algebraic form. (b) Compute the exact length of the walkway. Show every step in your calculation. (c) Give the length from part (b) to the nearest centimetre.

Related theory

Antiderivatives
Advanced Applications
Applications of Integration

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