Calculus Examples

$\int_{0}^{10} 0.3 x^{2} d x$

Step 1

Since $0.3$ is constant with respect to $x$ , move $0.3$ out of the integral.

$0.3 \int_{0}^{10} x^{2} d x$

Step 2

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

$0.3 (\frac{1}{3} x^{3}]_{0}^{10})$

Step 3

Simplify the answer.

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Step 3.1

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

$0.3 (\frac{x^{3}}{3}]_{0}^{10})$

Step 3.2

Substitute and simplify.

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Step 3.2.1

Evaluate $\frac{x^{3}}{3}$ at $10$ and at $0$ .

$0.3 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 3.2.2

Simplify.

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Step 3.2.2.1

Raise $10$ to the power of $3$ .

$0.3 (\frac{1000}{3} - \frac{0^{3}}{3})$

Step 3.2.2.2

Raising $0$ to any positive power yields $0$ .

$0.3 (\frac{1000}{3} - \frac{0}{3})$

Step 3.2.2.3

Cancel the common factor of $0$ and $3$ .

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Step 3.2.2.3.1

Factor $3$ out of $0$ .

$0.3 (\frac{1000}{3} - \frac{3 (0)}{3})$

Step 3.2.2.3.2

Cancel the common factors.

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Step 3.2.2.3.2.1

Factor $3$ out of $3$ .

$0.3 (\frac{1000}{3} - \frac{3 \cdot 0}{3 \cdot 1})$

Step 3.2.2.3.2.2

Cancel the common factor.

$0.3 (\frac{1000}{3} - \frac{3 \cdot 0}{3 \cdot 1})$

Step 3.2.2.3.2.3

Rewrite the expression.

$0.3 (\frac{1000}{3} - \frac{0}{1})$

Step 3.2.2.3.2.4

Divide $0$ by $1$ .

$0.3 (\frac{1000}{3} - 0)$

Step 3.2.2.4

Multiply $- 1$ by $0$ .

$0.3 (\frac{1000}{3} + 0)$

Step 3.2.2.5

Add $\frac{1000}{3}$ and $0$ .

$0.3 (\frac{1000}{3})$

Step 3.2.2.6

Combine $0.3$ and $\frac{1000}{3}$ .

$\frac{0.3 \cdot 1000}{3}$

Step 3.2.2.7

Multiply $0.3$ by $1000$ .

$\frac{300}{3}$

Step 3.2.2.8

Cancel the common factor of $300$ and $3$ .

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Step 3.2.2.8.1

Factor $3$ out of $300$ .

$\frac{3 \cdot 100}{3}$

Step 3.2.2.8.2

Cancel the common factors.

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Step 3.2.2.8.2.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 100}{3 (1)}$

Step 3.2.2.8.2.2

Cancel the common factor.

$\frac{3 \cdot 100}{3 \cdot 1}$

Step 3.2.2.8.2.3

Rewrite the expression.

$\frac{100}{1}$

Step 3.2.2.8.2.4

Divide $100$ by $1$ .

$100$

Step 4