Final answer:
To find the area of the surface formed by rotating the given curve about the y-axis, use the formula for the surface area of a solid of revolution.
Step-by-step explanation:
To find the area of the surface formed by rotating the given curve about the y-axis, we can use the formula for the surface area of a solid of revolution. The formula is:
A = 2π∫[a,b] x(y) * √(1 + (dy/dx)^2) dy
First, we need to express the curve in terms of y. Rearranging the equation y = 1/4x^2 - 1/2ln(x) gives us:
x = √(4(y + 1/8ln(4(y + 1/8))))
Next, we can find the derivative dy/dx and substitute it into the formula. Finally, evaluate the integral from the lower limit 2 to the upper limit 4 to get the area of the resulting surface.