# Thread: Integration along a path

1. ## Integration along a path

how do i approach this question please?

I dont understand the substitution from ds to dx.

thanks.

2. ## Re: Integration along a path

Hey BabyMilo.

Have you tried a contour integral by parametrizing the curve over some interval?

Standard parametrization for y = ax^2 + bx + c is to use the parameterization x = t and y = at^2 + bt + c.

Have you covered contour integration with parameterizations of a parabola?

3. ## Re: Integration along a path

The practical way of looking at it is

$ds^{2}=dx^{2}+dy^{2}=\left\{1+\left(\frac{dy}{dx} \right)^{2} \right\}dx^{2},$
so
$ds=\sqrt{1+\left(\frac{dy}{dx}\right)^{2}} \quad dx$

4. ## Re: Integration along a path

Originally Posted by chiro
Hey BabyMilo.

Have you tried a contour integral by parametrizing the curve over some interval?

Standard parametrization for y = ax^2 + bx + c is to use the parameterization x = t and y = at^2 + bt + c.

Have you covered contour integration with parameterizations of a parabola?
No i have not covered contour integration with parameterizations of a parabola.

But thanks.