The "rate of change" of a function is its derivative.
Extracted from Wikipedia's article on Derivative:>In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.
So, you are given the rate of change, that is the derivative, by integrating you'd find the primitive function which would be the amount of maple syrup.
It would probably be easier to understand if you think about it in terms of position and speed. The table says how fast you are moving, in miles per hour.
What is the antiderivative of speed? Position.
Question b is asking how much did your position change if you start at 5 mph for half an hour, then 4.5 mph for an hour and so on.
So basically,>a: the total amount of sap collected.>b: calculate it yourself, nigger.