I don't understand this integral

[0kelvin]

What did the teacher meant with this:

$$\int_{a}^{b} f(t)i + g(t)k dt $$

The two functions, a and b are all given. What is it to integrate a vector? From analytical geometry I know that something in the form of i + j + k is a vector.

 

[Mark44]

What did the teacher meant with this:

$$\int_{a}^{b} f(t)i + g(t)k dt $$

The two functions, a and b are all given. What is it to integrate a vector? From analytical geometry I know that something in the form of i + j + k is a vector.

Just integrate term by term. The i and k are the unit vectors $\hat i$ and $\hat j$. It probably makes more sense to write the integral as $$(\int_{a}^{b} f(t)dt) \hat i +(\int_{a}^{b} g(t) dt) \hat k $$