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

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1. Dec 30, 2016

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 ?

Last edited: Dec 30, 2016
2. Dec 30, 2016

### Dr. Courtney

You have to evaluate the dot product first.

3. Dec 30, 2016

### ZapperZ

Staff Emeritus
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.