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Math Help - How do you find the area for these parametric equations?

  1. #1
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    How do you find the area for these parametric equations?

    Find the area enclosed by the x-axis and the curve
    x = 1 + e^t , y = t - t^2

    The answer in the back of the book is: 3 - e

    I literally have spent about 2 hours on this problem, and I feel like I almost have the idea of how to do it.

    I set y = t - t^2 = 0 and came up with my values for t, which then gave me my x values for the boundary.

    Thus, I then took the integral of the area between my obtained t values of 1 and 0 for the following equation:

    (t-t^2)(e^t) dt

    I eventually obtained the value of e - 1, wtf?

    Please help...
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  2. #2
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    Joined
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    Quote Originally Posted by Brandong954 View Post
    Find the area enclosed by the x-axis and the curve
    x = 1 + e^t , y = t - t^2

    The answer in the back of the book is: 3 - e

    I literally have spent about 2 hours on this problem, and I feel like I almost have the idea of how to do it.

    I set y = t - t^2 = 0 and came up with my values for t, which then gave me my x values for the boundary.

    Thus, I then took the integral of the area between my obtained t values of 1 and 0 for the following equation:

    (t-t^2)(e^t) dt

    I eventually obtained the value of e - 1, wtf?

    Please help...
    Yeah so I doubled check my work and now I'm getting an answer of 0...
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  3. #3
    Super Member
    Joined
    Aug 2008
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    903
    \int_0^1 (t-t^2)e^t dt=3-e. Do the integration by parts.
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