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.

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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` ` `

=`piint_4^9[x^4-x]dx`

=`pi[1/5x^5-1/2x^2]_4^9`

`=pi[1/5*9^5-1/2*9^2-1/5*4^5+1/2*4^2]`

`=pi[1/5(9^5-4^5)-1/2(9^2-4^2)]`

`=11572.5*pi` cubic units.

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