Question regading integration (Volume generated)

[Sanosuke Sagara]

I have my question,solution,doubt in the attachment that followed.I hope that anyone will help me figure out this problem.Thanks for anybody that spend some time on this question.

 

[Sanosuke Sagara]

Help, I really need somebody to look out this question for me whether I have done wrong or not.I have my solution to the question in the attachment.

 

[Muzza]

I might be slightly paranoid, but why would I open a Word document from a complete stranger? Besides, there's a perfectly good way to write (mostly) anything you need here on the forum, using LaTeX.

 

[Sanosuke Sagara]

I don't know how to write equation in LateX form , so I post up the question with attachment.Trust me ,the ataachment don't have virus and won't affected your computer.

 

[Justin Lazear]

You crashed Word!

--J

(PS. Major accomplishment, but can't help ya' since I can't see it, sorry.)

 

[mathwonk]

can you ask your question in plain old words?

 

[Galileo]

The question asks to evaluate the volume generated by revolving the region S in the first quadrant, bounded by the coordinate axes , the line x=3 and the curve $y=\sqrt{1+x2}$ around the y-axis.

Check out this thread for LateX:
https://www.physicsforums.com/showthread.php?t=8997&highlight=latex
You can also click the latex equations from other posters to see the exact code used. It's fast and easy to learn this way. I advise making access to the problems easier if you want people to help you.

Anyway, you seem to have a made a slight mistake in calculating the 'total volume'
The volume generated by rotating the rectangle bounded by x=0, y=0, x=3 and y=$\sqrt{10}$ is $3^2\pi \sqrt{10}$, instead of $3 \pi \sqrt{10}$.

The volume use have to subtract is:
$$\pi \int_1^{\sqrt{10}}(y^2-1)dy=\pi\left[\frac{10\sqrt{10}}{3}-\sqrt{10}+2/3\right]$$
You got that part right.

If you subtract the above from $\pi 9\sqrt{10}$ you get the right answer.

 

[Sanosuke Sagara]

$\pi 9\sqrt{10}$

 

[Sanosuke Sagara]

Soory,I was just trying with the LateX equation and thanks for Galileo for seeking out the question for me and correct my errors.