SOLUTION: Find the VOLUME of the solid generated by revolving the region described about the indicated axis. 1. The region bounded by {{{ y = 3x - x^2 }}} and {{{ y = 0 }}} revolved about

Algebra ->  Volume -> SOLUTION: Find the VOLUME of the solid generated by revolving the region described about the indicated axis. 1. The region bounded by {{{ y = 3x - x^2 }}} and {{{ y = 0 }}} revolved about      Log On


   

Question 1025589: Find the VOLUME of the solid generated by revolving the region described about the indicated axis.
1. The region bounded by +y+=+3x+-+x%5E2+ and +y+=+0+ revolved about the x-axis
2. The region bounded by +y+=+x%5E3+, +y+=+0+, and +x+=+2+ revolved about the line +x+=+2+
3. The region bounded by +y+=+2x+-+x%5E2+ and the x-axis revolved about the line +y+=+2+
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1.
==> The antiderivative is 3x%5E3-%283x%5E4%29%2F2+%2B+x%5E5%2F5
==> The volume is pi%2A%283%2A3%5E3+-+%283%2F2%29%2A3%5E4+%2B+3%5E5%2F5+%29=+%2881pi%29%2F10
2.
==> The antiderivative is 4y+-+3y%5E%284%2F3%29+%2B+%283%2F5%29%2Ay%5E%285%2F3%29
==> The volume is pi%2A%284%2A8+-+3%2A8%5E%284%2F3%29+%2B%283%2F5%29%2A8%5E%285%2F3%29%29=+%2816pi%29%2F5

I leave the last one to you.