How do we compute an integral with a dot product inside ?

[mamadou]

I was trying to solve a problem involving work , as we know :
$$w = \int_{a}^{b} \vec{f}.d\vec{s}$$

but in my problem the path was cyrcular , so how to evaluate this kind of integral ?

 

[Dr. Courtney]

You have to evaluate the dot product first.

 

[ZapperZ]

I was trying to solve a problem involving work , as we know :
$$w = \int_{a}^{b} \vec{f}.d\vec{s}$$

but in my problem the path was cyrcular , so how to evaluate this kind of integral ?

First of all, this is math. Secondly, it is hard to know exactly why are you are not able to do this, because presumably, you should know how to do a line integral by the time you are taking such a course. You also didn't provide sufficient information of the problem.

Assuming that this a "circular" path, and that your origin is at the center of this circular path, then ds is simply the line element of the circle, i.e.

ds = r dθ θ

where θ is the unit vector in the angular direction. Refer to the figure below.

Then your integral limits will be the angles of the two end points.

Zz.