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Math Help - Find the area

  1. #1
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    Find the area

    Find the exact area of the surface obtained by rotating the given curves around the x-axis.

    x = 3t - t^2, y = 3t^2, 0 <= t <= 1

    My work:

    2pi * Integral from 0 to 1 of 3t^2 root[ ( 3-2t)^2 + (6t)^2)] dt

    2pi Int 0-->1 of 3t^2 root[ 40t^2 - 12t + 9]dt

    This can't be right...
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  2. #2
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    Quote Originally Posted by veronicak5678 View Post
    Find the exact area of the surface obtained by rotating the given curves around the x-axis.

    x = 3t - t^2, y = 3t^2, 0 <= t <= 1

    My work:

    2pi * Integral from 0 to 1 of 3t^2 root[ ( 3-2t)^2 + (6t)^2)] dt

    2pi Int 0-->1 of 3t^2 root[ 40t^2 - 12t + 9]dt

    This can't be right...
    I agree, recheck the problem statement. As it stands, the exact solution is one ugly ...
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  3. #3
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    I wrote to my professor and he told me it was a typo. It was supposed to be 3t - t^3. I was going to delete this post but I don't know how! Thanks for your help.
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