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Math Help - surface area of a light bulb

  1. #1
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    surface area of a light bulb

    can someone how to do this problem please?

    Find the surface area of an ornamental light bulb designed by revolving the graph of y=(1/3)x^(1/2)-x^(3/2), on the interval 0 to 1/3, about the x axis.
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  2. #2
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    Quote Originally Posted by BigPapa View Post
    can someone how to do this problem please?

    Find the surface area of an ornamental light bulb designed by revolving the graph of y=(1/3)x^(1/2)-x^(3/2), on the interval 0 to 1/3, about the x axis.
    I assume you're familiar with the formula and can calculate dy/dx.

    Start by showing that \sqrt{\left(\frac{dy}{dx} \right)^2 + 1} = \frac{1}{6} \left( x^{-1/2} + 9 x^{1/2}\right).

    The rest should by routine.
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  3. #3
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    I recommend we use a better looking lightbulb:

    f(x)=\begin{cases}0.211818 x^2 - 0.042646 x + 0.531034 & 0 \leq x \leq 1.88983 \\  \sqrt{1.35^2-(x-2.4913)^2} & 1.88983\leq x\leq 3.93\end{cases}
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