An antiderivative is an important concept in calculus that plays a key role in understanding the Fundamental Theorem of Calculus. Let's take a closer look.

The antiderivative of a function f(x) is a new function F(x), such that F'(x) = f(x). In simpler terms, the antiderivative of a function is like the reverse of taking the derivative. It allows us to determine the original function if we know its derivative.

For example, if f(x) = 3x^2, then F(x) = x^3 is an antiderivative of f(x) because its derivative, F'(x), equals 3x^2.

To find the antiderivative, we can use formulas and rules for basic functions, such as power, exponential, and trigonometric functions. For instance, the antiderivative of x^n is (x^(n+1))/(n+1).

The concept of antiderivatives is crucial because it leads us to the connection between differentiation and integration, as established by the Fundamental Theorem of Calculus.