Calculating Integrals with Vector Functions

[baermdr]

how does one calculate this integral.

[F(x)/||F(x)||]dx

where F in a function from a scalar to a vector.

 

[HallsofIvy]

how does one calculate this integral.

[F(x)/||F(x)||]dx

where F in a function from a scalar to a vector.

By integrating the individual components:

$$\int (f(x)\vec{i}+ g(x)\vec{j}+ h(x)\vec{k}) dx= \int f(x)dx \vec{i}+ \int g(x)dx \vec{j}+ \int h(x) dx \vec{k}$$