How do you find the volume of the solid generated by revolving the region bounded by the curves #y=x^2#, y=0 x=2 rotated about the x-axis?

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Answer 1 · 2015-08-30T16:22:56

See the explanation.

A at a value of #x# in #[0,1}#, a representative disk has radius #"top "y - "bottom "y# which will be #x^2-0=x^2#

Th volume of a disk is #pi r^2 * "thickness"#.

The thickness in this case is #dx#

Volume of slice: #pi(x^2)^2 dx#

Volume of the solid #int_0^1 pi(x^2)^2 dx#

We need:

#piint_0^1 x^4 dx = pi [x^5/5]_0^1#

# = pi[(1)^5/5 - (0^5)/5]#

# = pi/5#

The volume is #pi/5#