The goal of many engineering projects is to study the rate of change within a system. Measuring this change involves two processes: differentiation and integration.

Differentiation means determining the rate at which a curve is changing at a certain point in an equation. This can be achieved with a tool from calculus: the derivative.

To find this area with more accuracy, the curve is separated into smaller pieces. For example, if you were to find the area of Graph 1A in one large chunk, you would acheive less accuracy than in Graph 1B. The second graphs breaks down the area into smaller compartments and reduces the space left out. Integration means calculating the area under a curve.

It is relatively common for an engineer to figure out the area under a curve. Here are some cases when you could need the information:

A surveyor might need to know the area of a field bounded by a stream and two roads.

A water-resource engineer might need to know the cross-sectional area of a river to calculate flow rates.

A structural engineer might need to determine the net force due to a non uniform wind blowing against the side of a building.