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## Differential Calculus

This branch of calculus is used to compute various properties of integrals and derivatives of functions. Differential calculus is founded on infinitesimal differences summation. It covers areas such as differential equations and derivatives. The derivative of a given value is the level of change of the functions relative to the given value. Differential calculus is the process of finding the derivative of a function.

## The Theory of Calculus

This theory connects the concepts of functional integration and functional differentiation. This theory is fundamental in justifying the procedure. It computes the difference between the antiderivative at the lower and upper limits of the process of integration:

### First Theorem of Integral Calculus

This is the first part of the theory of calculus. It states that we can calculate one of the antiderivatives of a function as an integral of the function with integration that is variable bound. Meaning, there can be indefinite integrals for a continuous function.

### Second Theorem of Integral Calculus

The second theorem of integral calculus computes the difference between the value of the antiderivative at the upper limit and the same antiderivative value at the lower limit. This theorem offers a quick method of calculating the definite integral without estimating the limit of the sum.

## Integral Calculus

This is a branch of calculus that studies the attributes of integration and integrals. It is the inverse process differential calculus. Integration or anti-differentiation is used to find anti-derivatives. There are two classes of integration:

### Definite Integral

This class of integration has upper and lower limits. It is sometimes referred to as the Riemann integral.

### Indefinite Integral

It is a class of integration that is not defined by upper and lower limits. Indefinite integrals return a function of a variable that is independent.