change this function in terms of Y

[delgeezee]

Hi,
I need to find \(\displaystyle y=\frac{lnx}{\sqrt{x}}\) in terms of Y so that I have X isolated on one side.

 

[tkhunny]

Not possible. Why are you asked to do it?

 

[delgeezee]

Find the volume of the of the solid of revolution.
The region bounded by \(\displaystyle y=\frac{lnx}{\sqrt{x}}, y=0, x=2\) revolved around the X-axis

Woops!!! I thought the intersection of y=0 and \(\displaystyle y=\frac{lnx}{\sqrt{x}}\) was x=0, via grapging calculator. But at x=0, the function is undefined. But now I see that the intersection between y=0 and \(\displaystyle y=\frac{lnx}{\sqrt{x}}\) is actually x = 1

 

[tkhunny]

Hmmm... That is a vexing problem. You may wish to stick with Disks. It appears to be intractable with Shells.

Good work finding a tough one. There are numeric solutions, of course, but why?! Disks works just fine.