Substitution rule for vectorial functions

[Castilla]

You remember the substitution rule (or Change of variables theorem), when the integrand is some real function of real variable.

I would like to know if that rule has a version when the integrand is some vectorial function (of real variable).

Thanks for your attention.

 

[HallsofIvy]

Do you mean something like
$$\int (2(x-1)^2\vec{i}+ cos(x)sin(x)\vec{j}+ (2x+3)^2\vec{k})dx$$
You could look at each component separately: In the first component, let u= x-1, in the second, v= sin(x), in the third, w= 2x+3.

 

[Castilla]

Thanks, HallsofIvy. It worked.