Posted by **Becca** on Tuesday, January 24, 2012 at 12:59pm.

Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded by the curve y=x^2, below by the x-axis, and on the right by the line x=1, about the line x=-2

- Calculus -
**Steve**, Tuesday, January 24, 2012 at 1:40pm
Using shells,

v = Int(2πrh dx)[0,1]

where

r = x+2

h = y = x^2

2π*Int((x+2)x^2 dx)[0,1]

2π*Int(x^3 + 2x^2 dx)[0,1]

= 2π(1/4 x^4 + 2/3 x^3)[0,1]

= 2π(1/4 + 2/3) = 11π/6

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