Posted by **andy** on Thursday, July 18, 2013 at 12:14pm.

The area bounded by the curve 2y^2=x and the line 4y=x is rotated around the y-axis. The volume of the resulting structure can be expressed as V=a/bπ, where a and b are coprime positive integers. What is the value of a+b?

- calculus -
**Steve**, Thursday, July 18, 2013 at 12:29pm
something's wrong. The region is not closed.

- calculus -
**andy**, Thursday, July 18, 2013 at 12:36pm
i believe its bounded from y=0 to y=2

- calculus -
**Steve**, Thursday, July 18, 2013 at 12:41pm
Ah. In that case, using discs (washers),

v = ∫[0,2] π(R^2-r^2) dy

where R = 4y and r = 2y^2, so

v = ∫[0,2] π((4y)^2-(2y^2)^2) dy

= 4π∫[0,2] 4y^2 - y^4 dy

= 1024/15 π

- calculus -
**andy**, Thursday, July 18, 2013 at 12:45pm
no, i think that

∫[0,2] π((4y)^2-(2y^2)^2) dy is 256/15π

- calculus -
**Steve**, Thursday, July 18, 2013 at 12:57pm
you may be right. maybe I mixed in an unneeded factor of 4 somewhere.

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