Find an antiderivative of the function. (a) f(x)=2 x (b)...

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Key Concepts

Antiderivative

An antiderivative of a function is another function whose derivative is the given function. It represents the reverse process of differentiation and is central to the study of integral calculus, as it allows one to reconstruct a function from its derivative.

Integration

Integration is the mathematical process of finding an antiderivative. It is used to determine the accumulated total from a rate of change and is one of the fundamental operations in calculus, often involving techniques and rules that simplify the process.

Power Rule for Integration

The power rule for integration is a basic integration technique for functions of the form x^n. This rule states that the integral of x^n dx is x^(n+1)/(n+1) plus a constant, provided that n is not equal to -1. It is widely used for integrating polynomial functions.

Constant of Integration

When finding an antiderivative, an arbitrary constant, usually denoted as C, is added to the result. This reflects the fact that differentiating a constant results in zero, so there are infinitely many antiderivatives differing only by a constant.

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