What is the volume of the solid, if the area between the line through the points

Question

What is the volume of the solid, if the area between the line through the points P1 = (0,1) and P2= (pe/3, 2) and the graph of the functio n f(x) = sec(x) is rotated about the x- ais.

Explanation / Answer

THIS WILL HELP YOU Formulas to calculate the volume generated by revolving graphs of functions around one of the axes are given below. 1 - If f is a function such that f(x) >= 0 for all x in the interval [x1 , x2], the volume of the solid generated by revolving, around the x axis, the region bounded by the graph of f, the x axis (y = 0) and the vertical lines x = x1 and x = x2 is given by the integral Volume = x1 x2 p [ f(x) ] 2 dx 2 - If f and h are functions such that f(x) >= h(x) for all x in the interval [x1 , x2], the volume of the solid generated by revolving, around the x axis, the region bounded by the graphs of f and h, between x = x1 and x = x2 is given by the integral Volume = x1 x2 p [ f(x) 2 - h(x) 2] dx

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