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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- Dec 5th 2012, 01:29 AMDanthemathsIntegration 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 - Dec 5th 2012, 02:00 AMMarkFLRe: Integration Help (Read more for more info)
After expanding, you next want to integrate both sides with respect to

*x*. - Dec 5th 2012, 09:53 AMDanthemathsRe: 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? - Dec 6th 2012, 08:18 AMsjmillerRe: 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. - Dec 6th 2012, 08:36 AMHallsofIvyRe: Integration Help (Read more for more info)
Are you not taking a Calculus course? That surely looks like a Calculus question.

If $\displaystyle \frac{dy}{dx}= (x+3)(x-2)$, then $\displaystyle y= \int (x+3)(x- 2)dx$. 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.)