Defined Integral of a Vector-Valued Function

Topics: Vector-Valued Function

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(definition)

Let $r(t)=⟨r_1(t),\dots ,r_n(t)⟩$ be a vector-valued function.

We define the defined integral of $r(t)$ in the interval $t\in [a,b]$ as:

$${\int }_a^{b}rdt:=⟨{\int }_a^b{r}_{1}dt,\dots ,{\int }_a^b{r}_{n}dt⟩$$