Finding the area of a surface of revolution. Area of a surface of revolution for y = f(x). 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 r- axis is given by 1+ [f'(x))° dæ S = 2nf(x)/1+[f'(x)]² dz Part 1. Setup the integral that will give the area of the surface generated by revolving the curve ez +e z f(1) = -over the interval [0, In 5] about the r-axis. 2 S = Part 2. Calculate the area of the surface of revolution described above. S units squared.

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