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Math Help - first ever post:

  1. #1
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    first ever post:

    Hi. My name is Kelsey. I am a student at RIT currently taking project base calc 2. I am currently tasked with a rather challenging problem:


    Suppose R is the region bounded by the curves y = f(x) and y = c, on the interval from a to b. Find the value of c that minimizes the volume of the solid that is generated by revolving R about the line y = c.


    From what I can tell, it is an optimization problem looking to minimize volume: V = the integral from a to b of pi times (f(x)=c)2

    All Im looking for is a nudge in the right direction as to how I would solve this problem.
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  2. #2
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    Re: first ever post:

    Hello, KiloTango327!

    Suppose R is the region bounded by the curves y = f(x) and y = c, on the interval [a,b]
    Find the value of c that minimizes the volume of the solid that is generated by revolving R about the line  y = c.

    From what I can tell, it is an optimization problem looking to minimize volume: . V \:=\: \pi\int^b_a \big[f(x)-c\big]^2\,dx

    I'd say you understand the problem . . . and your game plan is correct.
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