A race track is described by the equations , and . How long is one lap around the track? Round your answer to the nearest tenth.
A) 16.6
B) 5.5
C) 33.1
D) 303.8

Question

A race track is described by the equations  , and  . How long is one lap around the track? Round your answer to the nearest tenth.
A) 16.6 
B) 5.5 
C) 33.1 
D) 303.8

Quizplus · Accepted Answer

We can find the length of one lap by finding the arc length of the curve. Using the formula for arc length, we have:

L = ∫sqrt[1+(dy/dx)^2] dx from x=0 to x=2π

L = ∫sqrt[1+(4sin(2x))^2] dx from x=0 to x=2π

This integral cannot be evaluated using elementary functions, so we must use numerical methods to approximate the answer. Using a calculator or computer program, we get:

L ≈ 33.1

Therefore, the best choice is C: 33.1.

A Race Track Is Described by the Equations