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how did we go from line 2 to 3?

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I get the 4y^2

but not the 81

We're rotating around the x-axis correct?

yes
I believe so

did I do it wrong?

oh shoot I'll do it again

I think eyad might have been rotating around the y-axis and finding surface area.

Wait, we want surface area and not volume.

In that case, we should be integrating \[\large 6\pi\int_2^6\left(\sqrt{x-2}\right)dx\]

I think you're right

why 6 pi

\[2\pi r\]But we can factor a 3 out of the r.

oh ok...lets see if I can do the integral

with my latex skills it's gonna be about 15 min just so you know

I've got plenty of time.

still working on it...

You're doing this using arc length?

I would not recommend that method.

No I thought that was for surface area

what method would you recommend?

I'm soo silly ...sorry

We would only solve for x if we're revolving around the y-axis.

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