• anonymous
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...
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert
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  • chestercat
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  • anonymous
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.

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