Mastering the Art of Integration: Vector-Valued Functions Explored
Integrating vector-valued functions involves computing the integral of functions whose outputs are vectors, typically represented as \(\int \mathbf{F}(t) dt\), where \(\mathbf{F}(t)\) could be a function from \(\mathbb{R}\) to \(\mathbb{R}^n\). This process requires taking the integral of each component function individually, often resulting in a vector of integrals. Applications include computing displacement from velocity in physics […]