Final answer:
To calculate the surface area of the solid generated by revolving the curve √y=4x around the x-axis, the formula for the surface area of a solid of revolution is used. However, the correct answer requires the limits of integration, which are not provided in the question.
Step-by-step explanation:
To find the surface area of the solid generated by revolving the curve √y=4x around the x-axis, we use the formula for the surface area of a solid of revolution. For a function y=f(x) revolved around the x-axis, the surface area S is given by:
S = 2π ∫_{a}^{b} f(x) √(1+[f'(x)]^2) dx
First, we write the given equation in terms of y: y = 16x^2. Then we find the derivative of y with respect to x, which is dy/dx = 32x. Plugging the function y = 16x^2 and its derivative into the formula and integrating:
S = 2π ∫ f(x) √{1+(32x)^2} dx
After performing the integration from the appropriate limits (which, based on the equation are from x=0 to x=√(y)/4), we calculate the surface area. However, to provide a correct answer, we need to know the limits of integration (or additional context to determine them), which are not specified in the question.