Average value, motion and accumulation in applied contexts

Learning objectives

Calculate the average value of a continuous function over an interval as the integral divided by the interval width, and interpret it graphically as the height of a rectangle of equal area

Recover position from velocity and velocity from acceleration by integrating and applying the given initial value

Distinguish displacement, the integral of velocity, from total distance traveled, the integral of speed, and compute each from a formula, a table or a graph

Solve an accumulation problem with a rate in and a rate out, finding the amount present at a given time and the time at which that amount is greatest or least, with a justification

Express net change as the definite integral of a rate of change, and interpret the result with correct units in the context of the question