Integral Calculus

Integral calculus is a very important branch of mathematic. A function has both a derivative and an integral in math calculus. The derivatives of a function are easier to find than the integrals of a function. The word integral is often used in place of antiderivatives. An integral table can help students find integrals in studying integral calculus. The process of finding integrals is called integration.

The integral of a function is donated by .

What is an integral of a function?

An integral of a math function is its antiderivative. Click here to read about antiderivatives.

Integral and antiderivative

In integral calculus, you can say:

The integral of f(x) = F(x) + C, or

The antiderivative of f(x) = F(x) + C

The two math sentences mean the exact same thing.

Indefinite integrals and definite integrals

Indefinite integrals are math integrals of a function whose constants are not limited to a certain range of values. Definite integrals, in contrast, are math integrals of a function where the value of C is specified. For example, let's examine a integral calculus problem below.

• Find the integral of F(x) = cos(x). Integral calculus problems such as this one ask the integral calculus students to find indefinite integrals of the function F(x).
• Find the integrals between a and b of F(x) = cos(x). Integral calculus problems such as this one ask the integral calculus students to find definite integrals of the function F(x) between value a and value b.