to find the

**total distance traveled**. FACT: FACT: EXAMPLE 1: Find the**total distance traveled**by a body and the body's displacement for a body whose velocity is v (t) = 6sin 3t on the time interval 0 ≤ t ≤ π /2. So to find the**total distance traveled**, I will have two integrals.Why is displacement different from distance?

**Distance**is a scalar quantity that refers to "how much ground an object has covered" during its motion.

**Displacement**is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

Is the total distance equal to the total displacement?

This artificial example shows that

**distance**and**displacement**have the same size only when we consider small intervals. Since the**displacement**is measured along the shortest path between two points, its magnitude is**always**less than or**equal**to the**distance**.