Integrals Consider a sphere rolling straight up an inclined plane.
If we plot the sphere's acceleration as a function of time, the graph would look something like the graph to the right. A line representing the Independent Variable at the lower bound. A line representing the Independent Variable at the upper bound. A curve representing the function being integrated. is a measure of the function integrated from the lower bound to the upper bound. Actually, in the case under consideration, the integration is telling us the change in velocity from the lower time to the upper time.