Calculus Examples

$f' (x) = x$

Step 1

The function $f (x)$ can be found by finding the indefinite integral of the derivative $f' (x)$ .

$f (x) = \int f' (x) d x$

Step 2

Set up the integral to solve.

$f (x) = \int x d x$

Step 3

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$\frac{1}{2} x^{2} + C$

Step 4

The answer is the antiderivative of the function $f' (x) = x$ .

$f (x) =$ $\frac{1}{2} x^{2} + C$