Calculus Examples

$4 + x$

Step 1

Write $4 + x$ as a function.

$f (x) = 4 + x$

Step 2

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 3

Set up the integral to solve.

$F (x) = \int 4 + x d x$

Step 4

Split the single integral into multiple integrals.

$\int 4 d x + \int x d x$

Step 5

Apply the constant rule.

$4 x + C + \int x d x$

Step 6

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

$4 x + C + \frac{1}{2} x^{2} + C$

Step 7

Simplify.

$4 x + \frac{1}{2} x^{2} + C$

Step 8

The answer is the antiderivative of the function $f (x) = 4 + x$ .

$F (x) =$ $4 x + \frac{1}{2} x^{2} + C$