Indefinitte Integral of Vector Valued Function

[Brunetto]

Hey all!

My calculus book goes through the proof/derivation of Kepler's first Law of planetary motion and I got to the part where the the indefinite integral of a vector valued function and got the answer plus the constant function. When the constant function was depicted in a diagram it was shown along the x-axis instead of along the vector of the answer. I guess the question I am asking is how to determine what direction the constant function points after computing an indefinite integral.

For example:

If

$\int$u' dt where u is a vector valued function

you get

u + c where c is a constant function.

How do you determine the direction that c points?

 

[Brunetto]

Is it arbitrary and it's just shown as falling along the x-axis for convenience?

 

[Brunetto]

Ok I figured it out...