Differentiation and integration are two fundamental concepts in calculus that deals with rates of change and the area under curves. They are closely related to each other and are used to solve a wide range of problems in science, engineering, and economics.

Differentiation is the process of finding the rate at which a function changes with respect to its input. In other words, it tells us how much a function is changing as we move along its input. We can think of differentiation as a kind of "slope-finding" process. For example, if we have a function that represents the position of an object as a function of time, we can differentiate it to find the velocity of the object, which is the rate at which it is changing position.  Integration, on the other hand, is the process of finding the area under a curve. We can think of integration as a kind of "accumulation" process. For example, if we have a function that represents the velocity of an object as a function of time, we can integrate it to find the total distance that the object has traveled over a certain period of time.

The relationship between differentiation and integration is given by the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes of each other. In other words, if we differentiate a function and then integrate the result, we will end up back at the original function (up to a constant). Similarly, if we integrate a function and then differentiate the result, we will end up with the original function (again, up to a constant).

This relationship is incredibly powerful and allows us to solve a wide range of problems in physics, engineering, and economics. For example, we can use differentiation and integration to analyze the motion of objects, to calculate the area under complex curves, to optimize functions, and to solve differential equations.

In summary, differentiation and integration are two fundamental concepts in calculus that are closely related to each other. Differentiation tells us how much a function is changing, while integration tells us how much area is under a curve. The relationship between them is given by the Fundamental Theorem of Calculus, which allows us to solve a wide range of problems in science, engineering, and economics.