Question

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?

Answer 1

Answer: 21.322

Explanation:

Integral from 0 to 2 of 2pi(2x+1)^1/2dx

Answer 2

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

`A= 2\pi \int_(0)^(2) √(2x) dx = (4 √(2) \pi)/(3) [x^(3/2)]_(0)^(2) = (16 \pi)/(3)`

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

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