Calculus Examples

$\int \sin (0 x) \cdot x^{2} d x$

Step 1

Multiply $0$ by $x$ .

$\int \sin (0) x^{2} d x$

Step 2

Since $\sin (0)$ is constant with respect to $x$ , move $\sin (0)$ out of the integral.

$\sin (0) \int x^{2} d x$

Step 3

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

$\sin (0) (\frac{1}{3} x^{3} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $\sin (0) (\frac{1}{3} x^{3} + C)$ as $0 (\frac{1}{3} x^{3}) + C$ .

$0 (\frac{1}{3} x^{3}) + C$

Step 4.2

Simplify.

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Step 4.2.1

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

$0 \frac{x^{3}}{3} + C$

Step 4.2.2

Multiply $0$ by $\frac{x^{3}}{3}$ .

$0 + C$

Step 4.2.3

Add $0$ and $C$ .

$C$