9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Finding Arc Lengths Of Curves Given By Parametric Equations — Quiz

Test your understanding of finding arc lengths of curves given by parametric equations with 5 practice questions.

Practice Questions

Question 1

For a curve given by the parametric equations $x=f(t)$ and $y=g(t)$ on $a \le t \le b$, which expression gives the arc length?

Question 2

A curve is given by $x=t$ and $y=t^2$ for $0 \le t \le 1$. What is its arc length?

Question 3

A particle moves according to $x=3t$ and $y=4t$ for $0 \le t \le 2$. What is the total distance traveled?

Question 4

Which integral represents the length of the curve given by $x=t^2$ and $y=t^3$ on $1 \le t \le 2$?

Question 5

A curve is parameterized by $x=\cos t$ and $y=\sin t$ for $0 \le t \le \pi$. What is its arc length?