Posted by **bob** on Friday, January 30, 2009 at 8:33pm.

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis.

y = 6 x^6 , y = 6 x , x >= 0

Find the volume V of this solid.

- calculus -
**drwls**, Friday, January 30, 2009 at 9:01pm
The curves intersect at x = 0 and x = 1. The region bounded between those curves has y-separation of 6(x-x^6).

For the total enclosed area, integrate that function times dx from x=0 to x=1.

- calculus (correction) -
**drwls**, Friday, January 30, 2009 at 9:06pm
I forgot that you wanted the volume of the solid obtained by rotating the curves about the x axis. This changes the formula to

Integral of 36 pi (x^2 - x^12) dx

...0 to 1

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