- Thread starter
- #1

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

- Thread starter Yuuki
- Start date

- Thread starter
- #1

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

- Admin
- #2

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

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

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

- Mar 1, 2012

- 249

Link

- Feb 15, 2012

- 1,967

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.