# Area, Volume, and Arc Length: Arc Length: Using and Abusing the Pythagorean Theorem True or False

 1 What is the length of the line segment between the points (2,1) and (5,7)? -> True False 2 The length of the curve of the function f(x) for a ≤ x ≤ b is -> True False 3 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]? -> 2.9 True False 4 On the interval [-2,2], the length of which curve is closest to 6.3? -> True False 5 Which integral gives the length of the curve f(x) = x3 + 2x2 on [-1,1]? -> True False 6 Which integral gives the length of the portion of the curve f(x) = x2 – 4x – 5 that lies below the x-axis? -> True False 7 What is the arc length, over the interval a ≤ t ≤ b, of a parametric curve described by the functions x(t) and y(t)? -> True False 8 Let x(t) = 3t and y(t) = -2t. What is the length of the curve described by these functions for -1 ≤ t ≤ 4? -> 5 True False 9 What is the length of the curve described by the equationsx(t) = t2 + 1y(t) = 4 – 3tbetween the points (2,1) and (5,10)? -> True False 10 What is the arc length of the polar function r = θ2 for α ≤ θ ≤ β? -> True False