SOLUTION: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
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Question 771777: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is a parabola with vertex at )
. 
is the horizontal line that passes through )
and that intersects the parabola, in the desired interval, at )
.
It will be convenient to write 
as a function of 
:
Rotate the parabola, then consider a thin disk with radius 
. The volume of this disk is ^2\,dy\ =\ \pi(y\ +\ 1)\,dy)
Integrate from -1 to 3
\ -\ \left(\frac{-1}{2}\ +\ (-1)\right)\right)\ =\ 9\pi)
John
My calculator said it, I believe it, that settles it
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