Chapter 6.1, Problem 20E

Position from velocity Consider an object moving along a line with the given velocity v and initial position

1. a. Determine the position function, for t ≥ 0, using the antiderivative method
2. b. Determine the position function, for t ≥ 0, using the Fundamental Theorem of Calculus (Theorem 6.1). Check for agreement with the answer to part (a).

20.     $v\left(t\right)=3\sin \pi t\text{ on }\left[0,4\right];s\left(0\right)=1$