Calculus Examples

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

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.

$F (x) = \int \frac{2 x^{2}}{1} d x$

Step 3

Divide $2 x^{2}$ by $1$ .

$\int 2 x^{2} d x$

Step 4

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int x^{2} d x$

Step 5

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$2 (\frac{1}{3} x^{3} + C)$

Step 6

Simplify the answer.

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Step 6.1

Rewrite $2 (\frac{1}{3} x^{3} + C)$ as $2 (\frac{1}{3}) x^{3} + C$ .

$2 (\frac{1}{3}) x^{3} + C$

Step 6.2

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} x^{3} + C$

Step 7

The answer is the antiderivative of the function $f (x) = \frac{2 x^{2}}{1}$ .

$F (x) =$ $\frac{2}{3} x^{3} + C$