Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^{5} and x=5sqrty about the y-axis over the interval [0,1].

Answer 1

assuming you mean 1<=x<=5, we have, using discs,

v = ∫[1,5] π(R^2-r^2) dx
where R=x^(1/5) and r=(x/5)^2