EXTRA CREDIT: +5 points
Ch 8.2 Day 2 Wkst AP Calc BC Name:
Arc Length and Surface Area
Objective: to use integrals to calculate arc length and surface area.
For a function, [pic], Arc Length =[pic].
For a function, [pic], rotated about the x-axis, Surface Area =[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 surface area of the solid obtained from rotating [pic] about the x-axis from x = 0 to x = 2 .
Example 3: 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 and Surface Area
For a function, [pic], Arc Length =[pic].
For a function, [pic], rotated about the x-axis, Surface Area =[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.
7. Find the surface area of the solid obtained from rotating [pic] about the x-axis from ( 1 , 1 ) to ( 4 , 2 ).
8. Find the surface area of the solid obtained from rotating [pic] about the x-axis from x = 1 to x = 2 .
9. Find the surface area if the arc from ( -3 , 4 ) to ( 3 , 4 ) of the equation, [pic], is revolved about the x-axis.
For problems #10 to #12, find the length of the parametric curves.
10. [pic] and [pic] for [pic]. NO CALCULATOR.
11. [pic] and [pic] for [pic]. NO CALCULATOR.
12. [pic] and [pic] for [pic]. CALCULATOR REQUIRED.
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Not an AP Topic
Not an AP Topic
[pic]
ANSWERS:
1) 3.526 7) 30.846
2) À 8) 51.882 (or 16,911 À/1024)
3) sinh 2 (or 3.627) 9) 188.496
4) 0.733 10) [pic]
5a) 15.865 11) e - 1
b)π 8) 51.882 (or 16,911 π/1024)
3) sinh 2 (or 3.627) 9) 188.496
4) 0.733 10) [pic]
5a) 15.865 11) e - 1
b) 18.850 (or 6π) 12) 5.180
6)
[pic]
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