Surface area of a loop rotated about the x-axis

[healthscience]

Hello,

I am stuck on this problem:

A figure shows a loop of the curve 32y² = x²(4-x²). Find the surface area generated by revolving this loop about the x-axis where x ∈ [0,2]

I don’t understand how to compute this surface area…

Can anyone help me out with that one?

Thank you!

 

[Dr.Peterson]

Hello,

I am stuck on this problem:



I don’t understand how to compute this surface area…

Can anyone help me out with that one?

Thank you!

Presumably you have been given the graph of the curve,



and can see that the surface area you want is generated by just the part in the first quadrant.

I would expect that you have either been taught how to find the surface area of a surface of revolution, or have searched for it (e.g. here). So the main problem may be that the curve is not written as a function of x. But you can solve for y, and then continue.

Or are you just having trouble with the integration?

Please show us where you are stuck. That is, what specific help do you need?

 

[mmm4444bot]

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