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Math Help - Integration

  1. #1
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    Integration

    Sorry for reposting...I think my previous post could not be viewed. X.x

    Q: A curve C is defined by the following pair of parametric equations:

    x = 1 + t^2 and y = \displaystyle{\frac{3 - t}{2+ t}} for 2 \1oq t \1oq 4. The region R is bounded by C, the x-axis and the lines x = 5 and x = 17.

    a) Find the exact area of the region R.

    b) Find V, the volume of solid generated when R is rotated through 2\pi about the x-axis.

    Please help! This is urgent! If possible, please include working and answers so I can compare with what I have done...Thank you very much!
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  2. #2
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    Quote Originally Posted by Tangera View Post
    Sorry for reposting...I think my previous post could not be viewed. X.x

    Q: A curve C is defined by the following pair of parametric equations:

    x = 1 + t^2 and y = \displaystyle{\frac{3 - t}{2+ t}} for 2 \1oq t \1oq 4. The region R is bounded by C, the x-axis and the lines x = 5 and x = 17.

    a) Find the exact area of the region R.

    b) Find V, the volume of solid generated when R is rotated through 2\pi about the x-axis.

    Please help! This is urgent! If possible, please include working and answers so I can compare with what I have done...Thank you very much!
    a) Area = \int_{t_1}^{t_2} y \, dx.

    b) V = \pi \int_{t_1}^{t_2} y^2 \, dx.

    In each case you substitute y = \frac{3-t}{2+t} and x = 1 + t^2 \Rightarrow dx = 2t \, dt.

    And since you're bounded by the x-axis it follows that x = 5 \Rightarrow t_{1} = 2 and x = 17 \Rightarrow t = 4.
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  3. #3
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    Quote Originally Posted by Tangera View Post
    Sorry for reposting...I think my previous post could not be viewed. X.x

    Q: A curve C is defined by the following pair of parametric equations:

    x = 1 + t^2 and y = \displaystyle{\frac{3 - t}{2+ t}} for 2 \1oq t \1oq 4. The region R is bounded by C, the x-axis and the lines x = 5 and x = 17.

    a) Find the exact area of the region R.

    b) Find V, the volume of solid generated when R is rotated through 2\pi about the x-axis.

    Please help! This is urgent! If possible, please include working and answers so I can compare with what I have done...Thank you very much!
    This thread http://www.mathhelpforum.com/math-he...ation-2-a.html

    clearly suggests where you were stuck with part b). Please don't start a new thread with questions that are relevant to an existing thread.
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