Measuring the Length of a Parabolic Path with Line Integral

[wasi-uz-zaman]

Hi experts
what is line integral - for example if I can draw graph of parabola and i can calculate the area under the graph. But how can i measure the length of parabolic path.

 

[mathman]

Let s be arc length. Then the differential of arc length is given by:

ds=√(dx²+dy²)=√(1+(dy/dx)²)dx.

To get the arc length between 2 values of x, integrate ds between those values.

 

[paulfr]

Two entirely different concepts
A line integral is more complex idea than the area under a curve in 2 dimensions.
It is done in 3 dimensions [or more]
The arc length is an application of integration in 2 D and the formula was given to yoou in the previous post.

 

[wasi-uz-zaman]

thanks a lot you have solved my query.