Integrating Vector-Valued Functions

#9.5 Integrating Vector-Valued Functions

By now, you should have a good understanding of vector functions. It’s alright if you don’t, for a refresher you can read our 9.4 study guide which talks about defining and differentiating vector-valued functions. This will help you understand this study guide and new concept easier!

Integrating these vector-valued functions allows us to go backward when relating the movement of a particle to its equation. For example, let's say we have a vector-valued function that gives the acceleration of a particle moving in space. A question asks us to determine the velocity of said particle. This means we need ✨integration✨

#💭 Integrating Vector-Valued Functions

It’s good to first recognize the format of your function. It is either written in two or three dimensions; we want to know which one so that we are not confused about which terms should be paid attention to when integrating.

A two-dimension vector function might look like this:

$$r(t)=f(t)i+g(t)j$$

or like this:

$$r(t)=⟨f(t),g(t)⟩$$

These both mean the same thing! 🪄

#❓ How do we integrate?

Luckily, we integrate each component of a vector function separate...