MHB Practice Problems for Surface Area and Volume of Rotation Integration

[annie122]

i notice i have much problem solving questions regarding surface areas and volumes of rotation.
it's not so much the setting up of the integration but i can't do the computing.

can you guys suggest online practice problems to do integration required in these kinds of problems??

thanks :)

 

[MarkFL]

Re: need advice on integration

i notice i have much problem solving questions regarding surface areas and volumes of rotation.
it's not so much the setting up of the integration but i can't do the computing.

can you guys suggest online practice problems to do integration required in these kinds of problems??

thanks :)

Do a search here on the word "revolution" and you will see many worked problems concerning solids and surfaces of revolution. :D

You could use these problems as practice problems and then compare your results with those posted.

 

[SuperSonic4]

VBulletin search software isn't always that good so you can use google to search this site by adding site:http://mathhelpboards.com to your search

Link

 

[Deveno]

Here's one to get you started:

Find the volume of the solid of revolution of the region bounded by:

$f(x) = \sqrt{r^2 - x^2}$

and the $x$-axis, rotated about the $x$-axis.

Do the disk method first, then the shell method. One will be lots easier.

(Hint: for the shell method, note that the solid obtained is the same one we obtain by taking twice the volume of the solid obtained by rotating the area bounded by:

$f(x) = \sqrt{r^2 - x^2}$, the $x$-axis, and the $y$-axis about the $y$-axis.

This allows you to integrate over $x$ instead of over $y$).

The "answer" to this problem is well-known and thus it should be easy for you to check your work.