The domed roof of a silo is made by revolving the curvey=f(x) = 10 cos(π10x),  a= 0m≤x≤5m=b,about the verticaly-axis along the centerline?

The domed roof of a silo is made by revolving the curve y=f(x) = 10 cos(π10x),  a= 0m≤x≤5m=b,about the vertical y-axis along the centerline of the silo.  The surface area,S that is obtained by revolving a curve y=f(x) in the domain from a to b around the y-axis can be calculated from the integral S= 2π∫bax√1 + [f′(x)]2dx. Calculate the surface area of the domed roof using Simpson’s 1/3 method, and divide the domain into eight equally-sized subintervals.  Use hand calculations to set up the general form of the problem, and use Python, MATLAB, or Math-ematica to perform the function evaluations and obtain the numerical value of the integral.