Simpson's Volume of Revolution (1 Viewer)

[Lukybear]

The section of the curve y=4/x^(1/2) from x= 1 to x =5 is rotated about the x axis. Use simpson's rule with 4 sub-interavals to find the volume of the solid of revloution formed. (4sigs).

How do we attempt at this?

 

[jet]

Find the expression for volume. It will contain an integral. Work out that integral with simpson's and substitute it back into the expression for voluime and voila! there's your answer

 

[Lukybear]

Hmmm... I dont think thats what they are asking. Otherwise i might just dont understand what you are saying.

Your suppose to use a table to find the volume. Cause that function, 4/x^(1/2) is integrateble at my level...

EDIT: Actually scrap that last bit. Its integrateable, but it wasnt assumed knowledge. So using simpsons is the only method.

 

[jet]

Remember the formula for volume between a curve and the x-axis?



So, substituting everything in, you get:



Use Simpson's rule to evaluate



And then substitute this back into the expression for volume. There's your answer.

 

[Lukybear]

Thanks a million. That seems so simple, but my inferior mind just could not comprehend it.