Integration

Definition

The process of finding a function, given its derivative, is called anti-differentiation (or integration). If F'(x) = f(x), we say F(x) is an anti-derivative of f(x).

Examples

F(x) =cos x is an anti-derivative of sin x, and e^x is an anti-derivative of e^x.

Note that if F(x) is an anti-derivative of f(x) then F(x) + c, where c is a constant (called the constant of integration) is also an anti-derivative of f(x), as the derivative of a constant function is 0. In fact they are the only anti-derivatives of f(x).

We write f(x) dx = F(x) + c.

if F'(x) = f(x) . We call this the indefinite integral of f(x) .

Thus in order to find the indefinite integral of a function, you need to be familiar with the techniques of differentiation.

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