Calculus Examples

$f (x) = - 11 x$

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.

$F (x) = \int - 11 x d x$

Step 3

Since $- 11$ is constant with respect to $x$ , move $- 11$ out of the integral.

$- 11 \int x d x$

Step 4

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

$- 11 (\frac{1}{2} x^{2} + C)$

Step 5

Simplify the answer.

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Step 5.1

Rewrite $- 11 (\frac{1}{2} x^{2} + C)$ as $- 11 (\frac{1}{2}) x^{2} + C$ .

$- 11 (\frac{1}{2}) x^{2} + C$

Step 5.2

Simplify.

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Step 5.2.1

Combine $- 11$ and $\frac{1}{2}$ .

$\frac{- 11}{2} x^{2} + C$

Step 5.2.2

Move the negative in front of the fraction.

$- \frac{11}{2} x^{2} + C$

Step 6

The answer is the antiderivative of the function $f (x) = - 11 x$ .

$F (x) =$ $- \frac{11}{2} x^{2} + C$