Question

Find the volume of the solid of revolution generated by rotating around the x-axis the region bounded by y=3^x-x^2 and y=0...

Answer 1

it is better to use disc method to find the volume in this particular case. take any point x then for that point your y will be given according to your equation if you rotate it , it will generate a disc of radius y. for an interval dx the volume will be pi*y^2*dx. you have to find the total area , in that case you have to integrate it .
\[\int\limits_{}^{} \pi*y ^{2}*dx= \int\limits_{}^{} \pi*(3^{x}-x ^{2})^{2}*dx\]
i have not use any limit when doing the integration . you can choose your limit. it is better no to choose x=infinity as it will give your area infinity.