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Math Help - surface integral

  1. #1
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    surface integral

    Find surface area given when rotating y=(x+5)^{\frac{1}{2}} and 5^{\frac{1}{2}} \leqslant x \leqslant 3 around y asis.
    How do i do this? Any help
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  2. #2
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    Re: surface integral

    Where did you get this problem? If you are taking a Calculus class in which you are given a problem like this, you should have learned several ways to do problems like this. The simplest, for this problem, is the "disk method". For a specific y value, x= y^2- 5 and the radius of the circle, when rotated around the y-axis, is x. The area of that circle is \pi x^2= \pi(y^2- 5)^2= \pi(y^4- 10y^2+ 25). Taking "dy" as the thickness of the disk, the volume is \pi(y^2- 10y+ 25). Integrate that. (I suspect that your limits are intended to be 5^{1/2}\le y\le 3. Check it.)
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  3. #3
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    Re: surface integral

    Yep, i see now. Thank you very much , now i realize it. We had almost same problem also.
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