When the vector-valued velocity function is integrated with respect to to obtain the…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

When the vector-valued velocity function

\mathbf v(t)

is integrated with respect to

t

to obtain the position function

\mathbf r(t)

, what additional term must be included in the antiderivative to account for the unknown initial position?