Find the Anti-Derivative 2x^2

$2 x^{2}$

Write $2 x^{2}$ as a function.

$f (x) = 2 x^{2}$

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

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

Set up the integral to solve.

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

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

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

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

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

Simplify the answer.

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Simplify.

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

Simplify.

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Combine $\frac{1}{3}$ and $x^{3}$ .

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

Combine $2$ and $\frac{x^{3}}{3}$ .

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

Reorder terms.

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

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

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

Find the Anti-Derivative 2x^2

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