Y axis rotation volume, is it infinite? y = 1/sqrt(x^3 + 3x}, 0 < x < 1, rotated around y-axis

[isakr1111]

I have a problem where i am a) Supposed to get an expression for the volume of

$\qquad y = \dfrac{1}{\sqrt{x^3 + 3x\;}},\quad 0<x<1$

...rotated around the y-axis.

This i got to $\dfrac{x}{\sqrt{x^3 + 3x\;}}$ by using the shell method. I believe this is correct but if it isn't, do let me know.

The b) task is where i am stuck, the task is to find out wheter the volume is infinte or not.
I have tried using substitution and gotten the answer that it is not, but i do know whether this is correct,

All help is appreciated.

 

[BigBeachBanana]

I have a problem where i am a) Supposed to get an expression for the volume of
View attachment 35709 Rotated around the y-axis. This i got to x/sqrt(x^3+3x) by using the shell method. I believe this is correct but if it isn't, do let me know.

The b) task is where i am stuck, the task is to find out wheter the volume is infinte or not.
I have tried using substitution and gotten the answer that it is not, but i do know whether this is correct,

All help is appreciated.

You're partially correct or just incomplete.

$$V= 2\pi \int_{0}^{1}\dfrac{x}{\sqrt{x^3+3x} }~ dx$$
You said you got an answer. What is it? Can you show your work?