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Math Help - show by intergration that the equation of the curve is y=...

  1. #1
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    show by intergration that the equation of the curve is y=...

    Hi

    another q.

    The diagram shows a curve for which  \frac{dy}{dx}\ =  - \frac{k}{k^3} where k is a constant. the curve passes through the points (1,18) and (4,3).

    Show by intergration that the equation of the curve is  y = \frac{16}{x^2}\ +2
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  2. #2
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    Quote Originally Posted by pederjohn View Post
    Hi

    another q.

    The diagram shows a curve for which  \frac{dy}{dx}\ =  - \frac{k}{k^3} where k is a constant. the curve passes through the points (1,18) and (4,3).

    Show by intergration that the equation of the curve is  y = \frac{16}{x^2}\ +2
    I assume you mean
     \frac{dy}{dx}\ =  - \frac{k}{x^3}
    \Rightarrow y = -k\int x^{-3}dx
    =-k\frac{x^{-2}}{(-2)}+c

    =\frac{k}{2x^2}+c

    Plug in the two pairs of values (1, 18) and (4,3), and solve the resulting simultaneous equations for k and c.

    Can you complete it now?

    Grandad
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