Ab L.

asked • 09/30/16

y= -x^2+6x-8 , y=0; about the x- axis What is the volume?

I got an answer. I want to make sure it's correct.

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John D. answered • 09/30/16

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I assume since it's calculus 2 that you're talking about a volume of a solid of revolution.  First, find the x-intercepts (2 and 4).  Then, use the integral for the volume of solid of revolution (pi * integral from 2 to 4 of f(x)^2 dx). 
 
Skipping the horrible and awful algebra gives an answer of 16pi/15.
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David S.

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I don't follow how this function has any x-intercepts.  The parabola is open down and the interval for integration has not been bounded.  I begin to see how your explanation might apply if the first term of the polynomial were x2 not -x2. Even then the sign of the x-intercepts you've given are both positive; I'm not seeing how this supports getting the -8 y-intercept.
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10/02/16

David S.

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Proper factoring has cleared up the issue noted above.  Please disregard.
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10/02/16

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