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Ch 8.2 Day 2 Wkst AP Calc BC Name:

Arc Length of Normal Functions and Parametric Equations

Objective: to use integrals to calculate arc length of normal functions and parametric equations.

For a function, [pic], Arc Length =[pic].

For parametric equations, [pic] and [pic], Arc Length = Distance Traveled

= [pic].

= [pic].

Example 1: Find the arc length of [pic] from x = 0 to x = 2 [pic]

Example 2: Find the length of the parametric curve for [pic] and [pic] for [pic].

Ch 8.2 Day 2 Wkst AP Calc BC Name:

Arc Length of Normal Functions and Parametric Equations

For a function, [pic], Arc Length =[pic].

For parametric equations, [pic] and [pic], Arc Length = Distance Traveled

= [pic].

= [pic].

Find the arc length of the graph of the function from x = 0 to x = 2 .

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. Consider the ellipse [pic].

a) Find the circumference the ellipse.

b) Find the area of the ellipse.

6.

For problems #10 to #12, find the length of the parametric curves.

7. [pic] and [pic] for [pic]. NO CALCULATOR.

8. [pic] and [pic] for [pic]. NO CALCULATOR.

9. [pic] and [pic] for [pic]. CALCULATOR REQUIRED.

-----------------------

[pic]

ANSWERS:

1) 3.526 7) [pic]

2) π 8) e - 1

3) sinh 2 (or 3.627) 9) 5.180

4) 0.733

5a) 15.865

b) 18.850 (or 6π)

6)

[pic]

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