Paul's Online Math Notes
Calculus II (Assignment Problems) / Parametric Equations and Polar Coordinates / Surface Area with Parametric Equations   [Notes] [Practice Problems] [Assignment Problems]

Calculus II - Assignment Problems
Applications of Integrals Previous Chapter   Next Chapter Series & Sequences
Arc Length with Parametric Equations Previous Section   Next Section Polar Coordinates

 Surface Area with Parametric Equations

For all the problems in this section you should only use the given parametric equations to determine the answer.

 

For problems1  4 determine the surface area of the object obtained by rotating the parametric curve about the given axis.  For these problems you may assume that the curve traces out exactly once for the given range of t’s.

 

1. Rotate   about the x-axis.

 

2. Rotate   about the y-axis.

 

3. Rotate   about the y-axis.

 

4. Rotate   about the x-axis. 

 

For problems 5  7 set up, but do not evaluate, an integral that gives the surface area of the object obtained by rotating the parametric curve about the given axis.  For these problems you may assume that the curve traces out exactly once for the given range of t’s.

 

5. Rotate   about the x-axis.

 

6. Rotate   about the y-axis.

 

7. Rotate   about the x-axis.

 

Arc Length with Parametric Equations Previous Section   Next Section Polar Coordinates
Applications of Integrals Previous Chapter   Next Chapter Series & Sequences

Calculus II (Assignment Problems) / Parametric Equations and Polar Coordinates / Surface Area with Parametric Equations    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2017 Paul Dawkins