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Math Help - Find equation of a curve

  1. #1
    Junior Member Lonehwolf's Avatar
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    [Solved]Find equation of a curve

    Been working on revision and still waiting on my mate to bring me the notes, so in the meantime I wouldn't like stalling, anyways this is the question

    Find \int{\frac{1}{x^2}dx}

    The gradient of a curve is given by \frac{dy}{dx}=\frac{1}{x^2}. Find the equation of the curve, given that it passes through the point (1,3).
    Last edited by Lonehwolf; March 22nd 2009 at 08:14 AM. Reason: solved
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Lonehwolf View Post
    Been working on revision and still waiting on my mate to bring me the notes, so in the meantime I wouldn't like stalling, anyways this is the question

    Find \int{\frac{1}{x^2}dx}

    The gradient of a curve is given by \frac{dy}{dx}=\frac{1}{x^2}. Find the equation of the curve, given that it passes through the point (1,3).
    \int{x^{a}dx}=\frac{x^{a+1}}{a+1} +C ~

    \int{\frac{1}{x^2}dx}=~\int{x^{-2}dx}=\frac{x^{-2+1}}{-2+1} +C

    Thus equation of such curves = \frac{x^{-1}}{-1} +C

    This curve passes through (1,3)

    So  3 = \frac{(1)^{-1}}{-1} +C

     3 = -1 +C \qquad \implies C= 4

    \frac{-1}{x} +4 is the requirement
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