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Math Help - Find the area enclosed by the parametric curve

  1. #1
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    Find the area enclosed by the parametric curve

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

    My work:

    ln(x-1) = t

    y = ln (x-1) - (ln (x-1))^2

    Area = Integral from 2 to e+1 of (t-t^2)(e^t) dt

    After integrating I get e^t(1+t-t^2) from 0 to e+1

    Which turns out to be something like -10. What am I doing wrong?
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  2. #2
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    Quote Originally Posted by veronicak5678 View Post
    Find the area enclosed by the x-axis and the curve x = 1+e^t, y = t-t^2

    My work:

    ln(x-1) = t

    y = ln (x-1) - (ln (x-1))^2

    Area = Integral from 2 to e+1 of (t-t^2)(e^t) dt x goes from 2 to e+1.

    After integrating I get e^t(1+t-t^2) from 0 to e+1 But t goes from 0 to 1.

    Which turns out to be something like -10. What am I doing wrong?
    ..
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  3. #3
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    Got it. Thanks for answering!
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