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Math Help - Area of a Surface of Revolution

  1. #1
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    Area of a Surface of Revolution

    Calculate the area when \frac{x^2}{4}+\frac{y^2}{2}=1 is rotated around the y-axis.


    This is the formula. A_y =2\pi\int_a^b x \sqrt{1+\left(\frac{dx}{dy}\right)^2} \, dy But when I solve for y, I get a . Should I just take the +version?
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  2. #2
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    Re: Area of a Surface of Revolution

    Replacing y by -y will just change dx/dy to -dx/dy and that is squared in your formula. So it really doesn't matter whether you use "y" or "-y".
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  3. #3
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    Re: Area of a Surface of Revolution

    Attempt:

    \frac{dx(y)}{dy} = -2y \centerdot (1 - \frac{y^2}{2})^{-1/2}

    and

    \left({\frac{dx(y)}{dy}}\right)^2 = \frac{4y^2}{1-\frac{y^2}{2}}
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  4. #4
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    Re: Area of a Surface of Revolution

    I have narrowed this down to finding the primitive of \sqrt{2+y^2} but I'm stuck there.
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