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# Area, Volume, and Arc Length

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

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Area, Volume, and Arc Length**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*isQ. 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*) =

*x*

^{3}– 4

*x*

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?