Question

Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0 <= x <= 4, about the x-axis.

Okay, so I've set up the integral like this: 2pi ∫[0,4] (3 sqrt (x))(sqrt(1+(1/4x)))dx Which is coming out to 108.5, but that's not giving me the right answer. Can you help me set up the integral correctly or tell me what I'm doing wrong?

Answer 1

The first Pappus theorem is formulated as
dA = 2πR*dS
where R is the distance between the centroid of the plane to the line of revolution.
I provided you an image how it's solved.
Mistakes:
R and the vertical strip there are shown. Distance from the centroid going to the line of revolution is simply half of the strip, that's why R = y/2
Your (y')² is not 1/4x, it should be 9/4x as being simplified. Just see on the image instead.