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Math Help - Surface area generated by rotating curve around y-axis

  1. #1
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    Surface area generated by rotating curve around y-axis

    I'm having a spot of trouble with this problem:

    Find the surface area generated by rotating the given curve about the y-axis.
    x=(e^t)-t
    y=4e^(t/2)
    0<t<8

    My homework is submitted online, and I keep working this problem out but it says I have it wrong, but I'm pretty sure I'm doing it right.

    I know A(s) = integral from 0 to 8 of 2pi x(t)sqrt((dx/dt)^2+(dy/dt)^2)dt, but I keep messing up. Help!

    ...Maybe i'm using the wrong equation?
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  2. #2
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    Quote Originally Posted by DarthPipsqueak View Post
    I'm having a spot of trouble with this problem:

    Find the surface area generated by rotating the given curve about the y-axis.
    x=(e^t)-t
    y=4e^(t/2)
    0<t<8

    My homework is submitted online, and I keep working this problem out but it says I have it wrong, but I'm pretty sure I'm doing it right.

    I know A(s) = integral from 0 to 8 of 2pi x(t)sqrt((dx/dt)^2+(dy/dt)^2)dt, but I keep messing up. Help!

    ...Maybe i'm using the wrong equation?
    your integral set up is correct ... the surface area I get is quite large (a bit on the side of ridiculous going to t = 8)

    A = \pi(e^{16}-12e^8-69)
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  3. #3
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    I was getting very large numbers too! But this worked out fine, and I was able to figure out the integral. I think I went wrong with my algebra somewhere.
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