Finding the area of a surface of revolution. Area of a surface of revolution for y = f(z). Let f(z) be a nonnegative smooth function (smooth means continuously differentiable) over the interval [a, b]. Then, the area of the surface of revolution formed by revolving the graph of y = f(x) about the z-axis is given by S = [ * 2x(2) 1 + [f'(2)] dz Part 1. Setup the integral that will give the area of the surface generated by revolving the curve f(z) = = + S= Part 2. over the interval [4, 6] about the z-axis. 2 Calculate the area of the surface of revolution described above. Round answer to three decimal places. S = units squared.