EXTRA CREDIT: +5 points
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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