On MATLAB:

Consider on the interval [a,b], 0 =< a < b, the region between the x-axis and the graph of a continuous function f(x) (=>0). The area of this region is A = Integral a to b from f(x)dx. By rotating this region about the y-axis a solid is generated with volume V = intergal a to b from 2pix f(x)dx. Take [a,b] = [0,1] and f(x) = x sin(p x) with PARAMETER p. Find an analytical formula for Q = A/V as a function of p and draw this relation 0=< p =< pi as a red curve