The graph of the equation 2x=y^2 from a(0,0) to b(2,2) is rotated around the x axis. the surface area of the resulting solid is?

Write the given equation as
x = (1/2)y² or as y = √(2x)

Graph the given curve within the region (0,0) and (2,2) as shown in the figure below.
When the curve is rotated about the x-axis, an element of surface area is
dA = 2πy dx

The surface area of the resulting solid is


If the right end is considered, the extra area is π*(2²) = 4π

The surface area of the rotated solid is (16π)/3.
If the right end is considered, it is an extra area of 4π.