Think you’ve got your head wrapped around **Area, Volume, and Arc Length**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

Q. What is the length of the line segment between the points (2,1) and (5,7)?

2

3

9

Q. The length of the curve of the function *f*(*x*) for *a* ≤ *x* ≤ *b* is

Q. Consider the graph of the function *f*(*x*) below.

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

2.5

2.9

π

3.2

Q. On the interval [-2,2], the length of which curve is closest to 6.3?

Q. Which integral gives the length of the curve *f*(*x*) = *x*^{3} + 2*x*^{2} on [-1,1]?

Q. Which integral gives the length of the portion of the curve *f*(*x*) = *x*^{2} – 4*x* – 5 that lies below the *x*-axis?

Q. What is the arc length, over the interval *a* ≤ *t* ≤ *b*, of a parametric curve described by the functions *x*(*t*) and *y*(*t*)?

Q. Let *x*(*t*) = 3*t* and *y*(*t*) = -2*t*. What is the length of the curve described by these functions for -1 ≤ *t* ≤ 4?

5

Q. What is the length of the curve described by the equations

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

*y*(*t*) = 4 – 3*t*

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

Q. What is the arc length of the polar function *r* = θ^{2} for α ≤ θ ≤ β?