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Calculus is used in every branch of the (physic) sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.

It allows one to go from non-constant rates of change to the (totality) change or vice versa, and many times in studying a problem we know one and are trying to find the other.

Physics makes particular (usability) of calculus; all concepts in classical mechanics and electromagnetism are related through calculus.

The mass of an object of known (dense), the moment of inertia of objects, as well as the total energy of an object within a conservative field can be found by the use of calculus.

Maxwell's theory of electromagnetism and Einstein's theory of general (relate) are also expressed in the language of differential calculus.

Chemistry also uses calculus in determining (react) rates and radioactive decay.

In biology, (populate) dynamics starts with reproduction and death rates to model population changes.

It can be (use) with linear algebra to find the "best fit" linear approximation for a set of points in a domain.

In analytic geometry, the study of graphs of functions, calculus is used to find high points and low points (maxima and minima), slope, concavity and (inflect) points.

Green's Theorem, which gives the (relate) between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C, is applied in an instrument known as a planimeter, which is used to calculate the area of a flat surface on a drawing.

For example, it can be used to calculate the amount of area taken up by an (irregular) shaped flower bed or swimming pool when designing the layout of a piece of property.

In the realm of medicine, calculus can be used to find the optimal branching angle of a blood vessel so as to maximize flow. From the decay laws for a particular drug's (eliminate) from the body, it is used to derive dosing laws.

In nuclear medicine, it is used to build models of radiation transport in (target) tumor therapies.

In economics, calculus allows for the (determine) of maximal profit by providing a way to easily calculate both marginal cost and marginal revenue.