Which process involves calculating the total rate of change over a period?

The correct choice, integration, is fundamental for determining the total rate of change over a specified time interval. In calculus, integration is the process of summing infinitesimally small quantities to find a whole. It allows you to calculate areas under curves, which represent accumulated quantities, such as distance covered over time when velocity is given as a function of time.

For example, if you have a velocity function describing how speed changes over time, integrating this function over a specific time interval gives you the total distance traveled. This application highlights the essence of integration—it not only provides the total accumulated change but does so by considering the continuous nature of the functions involved.

The other choices—summation, analysis, and estimation—do not capture this concept in the same manner. Summation typically refers to adding discrete values together, while analysis involves examining data or trends without necessarily performing a calculation of total change. Estimation is about making a rough calculation or assessment and does not inherently involve the detailed calculation required to determine total rates of change over time as integration does.