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Math Help - Integration Help (Read more for more info)

  1. #1
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    Integration Help (Read more for more info)

    Hey guys,
    I am a bit stuck answering this question. The question being:
    If dy/dx = (x+3)(x-2), Find y

    I expanded the brackets first of all but a bit stuck from here. Can anyone give me some guidance on what to do next?

    Thanks
    Danthemaths
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Integration Help (Read more for more info)

    After expanding, you next want to integrate both sides with respect to x.
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  3. #3
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    Re: Integration Help (Read more for more info)

    do we get two answers? because x=-3 and another x=2

    thats the part i was stuck on, it there two answers to this question??
    coz once the brackets are expanded you get dy/dx=x^2-x-1
    integrate that you get: y=x^3/3-1
    then dont you sub each x in? so y= (-3)^3/3-1 and then sub the other in to get y=(2)^3/3-1

    and you get 2 y answers?

    is this how you do this?
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  4. #4
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    Re: Integration Help (Read more for more info)

    I'm assuming you want to determine f(x), a.k.a solving a differential equation. Note that the equation is separable: Pauls Online Notes : Differential Equations - Separable Equations

    Basically you need to get the differentials to be on separate side of the equality. Therefore dy = (x-2)(x+3)dx. Integrate both sides to get a general expression for f(x). I believe 'y" is referring to the solution of the differential equation in this question.
    Last edited by sjmiller; December 6th 2012 at 09:21 AM.
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  5. #5
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    Re: Integration Help (Read more for more info)

    Are you not taking a Calculus course? That surely looks like a Calculus question.
    If \frac{dy}{dx}= (x+3)(x-2), then y= \int (x+3)(x- 2)dx. Once you have multiplied (x+3)(x-2) that will be an easy integral.

    (There are not two solutions. There are, strictly speaking, an infinite number of solutions, one for each choice of the "constant of integration". But the fact that there two factors is not relevant.)
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