# Area, Volume, and Arc Length: Arc Length: Using and Abusing the Pythagorean Theorem Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Area, Volume, and Arc Length***f*(

*x*) for

*a*≤

*x*≤

*b*is

*f*(

*x*) below.

Which of the following could be the arc length of the function *f*(*x*) on the interval [-1,1]?

*g*(

*x*) = -2 –

*x*

*j*(

*x*) =

*x*

^{3}– 4

*x*

*f*(

*x*) =

*x*

^{3}+ 2

*x*

^{2}on [-1,1]?

*f*(

*x*) =

*x*

^{2}– 4

*x*– 5 that lies below the

*x*-axis?

*a*≤

*t*≤

*b*, of a parametric curve described by the functions

*x*(

*t*) and

*y*(

*t*)?

*x*(

*t*) = 3

*t*and

*y*(

*t*) = -2

*t*. What is the length of the curve described by these functions for -1 ≤

*t*≤ 4?

*x*(*t*) = *t*^{2} + 1

*y*(*t*) = 4 – 3*t*

between the points (2,1) and (5,10)?

*r*= θ

^{2}for α ≤ θ ≤ β?