Home » Blog » Find a function whose ordinate set generates a solid of revolution with volume x2 f(x)

Find a function whose ordinate set generates a solid of revolution with volume x2 f(x)

Let f(x) be a nonnegative, differentiable function whose graph passes through both points (0,0) and \left( 1, \frac{2}{\pi}\right). For every real number x > 0, the ordinate set of f on the interval [0,x] generates a solid of revolution when rotated about the x-axis whose volume is given by

    \[ x^2 f(x). \]

Find the formula for the function f(x).


Incomplete.

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):