I have a problem where i am a) Supposed to get an expression for the volume of
[imath]\qquad y = \dfrac{1}{\sqrt{x^3 + 3x\;}},\quad 0<x<1[/imath]
...rotated around the y-axis.
This i got to [imath]\dfrac{x}{\sqrt{x^3 + 3x\;}}[/imath] 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.
[imath]\qquad y = \dfrac{1}{\sqrt{x^3 + 3x\;}},\quad 0<x<1[/imath]
...rotated around the y-axis.
This i got to [imath]\dfrac{x}{\sqrt{x^3 + 3x\;}}[/imath] 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.
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