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Math Help - Integration problem

  1. #1
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    Unhappy Integration problem

    I am trying to integrate y.(dy/dx) wrt x

    I know the answer is (y^2)/2 but I don't know how to get the answer. Can someone please point me in the right direction
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  2. #2
    Member Ruun's Avatar
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    Re: Integration problem

    Is anything else than the chain rule:

    \frac{d}{dx}f(g(x))=\frac{df}{dg}\frac{dg}{dx}

    In your particular case f(x)=y^2(x), g(x)=y(x)


    \frac{d}{dx}y^2=2y\frac{dy}{dx}
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  3. #3
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    Re: Integration problem

    I'm sorry but I don't get it, can you elaborate a little more?
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  4. #4
    Member Ruun's Avatar
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    Re: Integration problem

    Let y(x) be any (differentiable) function of x. Do you know the derivative of y^2(x) with respect to x?
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  5. #5
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    Re: Integration problem

    Of course, 2y.(dy/dx)

    But I don't get how that relates to my specific problem. I appreciate your patience with me
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  6. #6
    Member Ruun's Avatar
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    Re: Integration problem

    You have the following equality

    \frac{d}{dx}y^2(x)=2y\frac{dy}{dx}

    If two things are the same, their integrals should also be the same. So, integrate both sides and see what happens to the left hand side of the equation
    Thanks from akhattab
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  7. #7
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    Re: Integration problem

    I get it! Clever way of solving the problem
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