




Calculate the surface area generated by rotating the curve around the xaxis.
Rotate the line
By rotating the line around the xaxis, we generate
a_{ }surface of revolution (a cone without its base.)
Rotate ds
We revolve around the xaxis an element of arc length ds.
This generates a thin strip of area dA.
Surface area of the cone
We get the surface area S of the cone by summing all the elements of area dA as dA sweeps along the complete surface, that is by integrating dA from x = 0 to x = 1.