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volume of solid of revolution

Hi I have to find volume of solids for f(x)= (1/x) cos(1/x) from x= 2/3pi to x= 2/pi and so far this is what I have done attached here as I don't know how to type all fancy stuff- so please have a look and any guidance in completeing this will be great

Re: volume of solid of revolution

Is this the volume of the region rotated about the x axis?

Re: volume of solid of revolution

yes - sorry I forgot to mention- it is rotated about x-axis

Re: volume of solid of revolution

First of all, your integral has been set up wrong... the volume of a region rotated about the axis is given by , so in this case

Now make the substitution , and note that when and so that the integral becomes

Go from here.

Re: volume of solid of revolution

thanks- I can see my error- Can I ask- how do you get this Math text on here as I alwats have to PDF and attached

Re: volume of solid of revolution

It's called LaTeX. You can learn more in the LaTeX subforum. Once you know the code, put it in tex tags.

Re: volume of solid of revolution

Hey I am clear up until -1/x^2 disapperars and replaced by 1/2+1/2(cos(2u)- can you please just clarify that please

Quote:

Originally Posted by

**Prove It** First of all, your integral has been set up wrong... the volume of a region rotated about the

axis is given by

, so in this case

Now make the substitution

, and note that when

and

so that the integral becomes

Go from here.

Re: volume of solid of revolution

. Can you see where is in your original integral? Replace it with .

Also, you should know that . Get everything in terms of cosines and solve it for .

Re: volume of solid of revolution

Yes I understand the identity replacement where you got 1/2(cos(2u) but you alos got extra 1/2 i.e. 1/2 +1/2c0s(2u) du that part is unclear- sorry about this but I am so new to all these

Re: volume of solid of revolution

Re: volume of solid of revolution

thanks for this- so now I am clear- where you say go from here- I need to find the integral of 1/2+1/2 cos(2u) right?

Re: volume of solid of revolution

Re: volume of solid of revolution

Quote:

Originally Posted by

**Prove It** Yes.

Many thanks for every help you offered I managed to find my answer and complete the task