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?
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 a ≤ t ≤ b, 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?
