Expert: Ahmed Salami - 6/3/2009

Question
the region R is a quadrant, is bounded by y=x^2, the y axis, and the line y=2.  where R is rotated about the y xis, the volume of the soild generated in cubic units is?

Answer
Hi Kristin,
The volume of solid formed when the area bounded by the curve y = f(x) is rotated about the y axis is the definite integral ∫πx²dy between the two y limits.
For this situation, the volume is
V = ∫πx²dy from y = 0 to y = 2
 = ∫πydy from y = 0 to y = 2
 = [πy²/2] from y = 0 to y = 2
 = [π2²/2] - [π0²/2]
 = 2π - 0
 = 2π cubic units

Regards