Final answer:
To find the area of the resulting surface when the given curve is rotated about the y-axis, use the formula for the surface area of revolution.
Step-by-step explanation:
To find the area of the resulting surface when the given curve y = 14x² - 12 ln(x) is rotated about the y-axis, we can use the formula for the surface area of revolution. The formula is:S = 2π∫(a to b) f(x)√(1 + (f'(x))²) dxIn this case, the given curve is y = 14x² - 12 ln(x), so we need to find the derivative of the curve: y' = 28x - (12/x)Now we can substitute the curve and its derivative into the formula and evaluate the integral to find the area of the resulting surface.