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Math Help - Surface Area obtained by rotating the curve

  1. #1
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    Surface Area obtained by rotating the curve

    Hi,

    My problem is: Find the area of the surface obtained by rotating the curve x = 5 e^{2y} from y=0 to y = 2 about the y-axis.

    I use the surface Formula: S = \int_a^b {2 \pi x} \sqrt{1+{x'}^2} dy

    but could do no more after plug in  {x'} = 10e^y


    Could anyone help me with this? THANKS!!
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  2. #2
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    x' = 10e^{2y}

    This is the second time today I have corrected this error. Someone must be teaching it wrong.

    P.S. How is Provo these days?
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    x' = 10e^{2y}

    This is the second time today I have corrected this error. Someone must be teaching it wrong.

    P.S. How is Provo these days?
    right, it should be x' = 10e^{2y},

    but problem is actually that I don't know how to deal with:

     \int 2 \pi 5e^{2y} \sqrt{1+100e^{4y}} dy after I applied the surface area formula to this question.
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  4. #4
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    If you resist the temptation to evaluate the square under the radical, a convenient substitution may come to mind.

    u = 10\cdot e^{2y} perhaps? Mind you, it's still not pretty. That's why we invented approximation techniques. Just one of these can be a total bear.
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