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May 3, 2015

May 3, 2015

Posted by **Beth** on Friday, December 2, 2011 at 11:42am.

- Calculus -
**Steve**, Friday, December 2, 2011 at 11:57amYou can use discs, integrating along y:

V = Int(pi (R^2 - r^2) dy)[0,1]

where R = y and r = sqrt(y)

= pi*Int(y - y^2)dy[0,1]

= pi(1/2 y^2 - 1/3 y^3)[0,1]

= pi(1/2 - 1/3)

= pi/6

Or, you can use shells, integrating along x:

V = Int(2pi*r*h dx)[0,1]

where r = x h = x-x^2

= 2pi*Int(x(x-x^2) dx)[0,1]

= 2pi(x^2 - x^3 dx)[0,1]

= 2pi(1/3 x^3 - 1/4 x^4)[0,1]

= 2pi(1/3 - 1/4)

= 2pi(1/12)

= pi/6

- Calculus -
**Beth**, Sunday, December 4, 2011 at 4:47pmRevolve the region bounded by y = 4x and y = x2 about the y-axis. In cubic units, the resulting volume is