Question

Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.
We have to use the surface area formula of revolution.
Integral (2pi*f(x)sqrt(1+f'(x)^2))dx

Answer 1

Use the first Pappus theorem for the surface area.
dA = 2πR(dS)
where R = the distance between the centroid of the surface plane to the line of revolution
dS = infinitesimal arc length
dA = infinitesimal area

We integrate it to get the whole surface area. For more info, refer on the image as you can see labels and solutions.