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 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.