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Area, Volume, and Arc Length

Area, Volume, and Arc Length

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)? ->
2. The length of the curve of the function f(x) for axb is ->
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

4. On the interval [-2,2], the length of which curve is closest to 6.3? ->
5. Which integral gives the length of the curve f(x) = x3 + 2x2 on [-1,1]? ->
6. Which integral gives the length of the portion of the curve f(x) = x2 – 4x – 5 that lies below the x-axis? ->
7. What is the arc length, over the interval atb, of a parametric curve described by the functions x(t) and y(t)? ->
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
9. 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)? ->

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

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