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, , Arc Length =.
For a function, , rotated about the x-axis, Surface Area =.
For parametric equations, and , Arc Length = Distance Traveled
= .
= .
Example 1: Find the arc length of from x = 0 to x = 2
Example 2: Find the surface area of the solid obtained from rotating about the x-axis from x = 0 to x = 2 .
Example 3: Find the length of the parametric curve for and for .
Ch 8.2 Day 2 Wkst AP Calc BC Name:
Arc Length and Surface Area
For a function, , Arc Length =.
For a function, , rotated about the x-axis, Surface Area =.
For parametric equations, and , Arc Length = Distance Traveled
= .
= .
Find the arc length of the graph of the function from x = 0 to x = 2 .
1. 2.
3. 4.
5. Consider the ellipse .
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 about the x-axis from ( 1 , 1 ) to ( 4 , 2 ).
8. Find the surface area of the solid obtained from rotating 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, , is revolved about the x-axis.
For problems #10 to #12, find the length of the parametric curves.
10. and for . NO CALCULATOR.
11. and for . NO CALCULATOR.
12. and for . CALCULATOR REQUIRED.