2 Attachment(s)

Calculate Volume using the Method of Cylindrical Shells - Urgent

Attachment 25095

Here are some things I have done. I already found the volume since the other part of the question said to use the method of discs/washers. It is 54.0633 cubic units (correct answer).

I found by trial and error that (since this is an online assignment) that a= 9/sqrt(82) and c =9 .

What do I do? Why should there be two integrals, I don't understand.

I have tried the following.

y = 9^x becomes x = lny/ln9

Formula

h = lny/ln9

r = y

So I got integral from 9/sqrt(82) to 9 of

Attachment 25096 dy

But that's just one integral and perhaps even incorrect. Please show me what to do.

Thanks

Re: Calculate Volume using the Method of Cylindrical Shells - Urgent

the sketch of the graph is misleading ...

note that , so there is a very small region between the curve and from to .

Re: Calculate Volume using the Method of Cylindrical Shells - Urgent

To evaluate the volume of your region, you need to do

The only one of those integrals which may cause you any trouble is the second, so do

which you would then evaluate using integration by parts twice. See how you go :)

Re: Calculate Volume using the Method of Cylindrical Shells - Urgent

Is this the method of cylindrical shells? I am obliged to use cylindrical shells. Can you use r (radius), h(height)? And why will my answer be in the form of a sum of two integrals (see the question -top of image)?

Re: Calculate Volume using the Method of Cylindrical Shells - Urgent

using the method of cylindrical shells ...

Re: Calculate Volume using the Method of Cylindrical Shells - Urgent