Antiderivative of a Vector-Valued Function

Definition

Finding an antiderivative (or integral) for each component of a vector-valued function independently yields an antiderivative for that entire function. It allows us to find the original vector-valued function given its derivative.

Analogy

Consider a group of friends who are walking in reverse, retracing their steps. Each friend represents a component of the vector, and finding the antiderivative is like figuring out their original positions by reversing their movements.

Related terms

Initial Condition: An initial condition specifies the value(s) of a function at a particular point or time.

Indefinite Integral: An indefinite integral represents a family of functions that differ only by a constant.

Constant Vector Function: A constant vector function has all its components equal to constants, resulting in no change as the independent variable varies.