1. Find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and y=x^1/2 and the lines x=4 and x=9 about the x-axis.
Volume of the solid obtained by rotating the region bounded by the curves y=f(x) and y=g(x) and the lines x=a and x=b about the x axis is given by :`int_a^b pi [f(x)^2-g(x)^2]dx`
=`int_4^9pi[(x^2)^2-(sqrtx)^2]dx` ` `
`=11572.5*pi` cubic units.