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

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 axb 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?

g(x) = -2 – x
j(x) = x3 – 4x
Q. Which integral gives the length of the curve f(x) = x3 + 2x2 on [-1,1]?

Q. Which integral gives the length of the portion of the curve f(x) = x2 – 4x – 5 that lies below the x-axis?

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

Q. Let x(t) = 3t and y(t) = -2t. 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) = t2 + 1

y(t) = 4 – 3t

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

Q. What is the arc length of the polar function r = θ2 for α ≤ θ ≤ β?