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Calculus Examples

\int_{- 1}^{0} - 3 x d x

$\int_{- 1}^{0} - 3 x d x$

Step 1

Since

- 3

$- 3$ is constant with respect to

x

$x$ , move

- 3

$- 3$ out of the integral.

- 3 \int_{- 1}^{0} x d x

$- 3 \int_{- 1}^{0} x d x$

Step 2

By the Power Rule, the integral of

x

$x$ with respect to

x

$x$ is

\frac{1}{2} x^{2}

$\frac{1}{2} x^{2}$ .

- 3 (\frac{1}{2} x^{2}]_{- 1}^{0})

$- 3 (\frac{1}{2} x^{2}]_{- 1}^{0})$

Step 3

Simplify the answer.

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Step 3.1

Combine

\frac{1}{2}

$\frac{1}{2}$ and

x^{2}

$x^{2}$ .

- 3 (\frac{x^{2}}{2}]_{- 1}^{0})

$- 3 (\frac{x^{2}}{2}]_{- 1}^{0})$

Step 3.2

Substitute and simplify.

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Step 3.2.1

Evaluate

\frac{x^{2}}{2}

$\frac{x^{2}}{2}$ at

0

$0$ and at

- 1

$- 1$ .

- 3 ((\frac{0^{2}}{2}) - \frac{{(- 1)}^{2}}{2})

$- 3 ((\frac{0^{2}}{2}) - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2

Simplify.

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Step 3.2.2.1

Raising

0

$0$ to any positive power yields

0

$0$ .

- 3 (\frac{0}{2} - \frac{{(- 1)}^{2}}{2})

$- 3 (\frac{0}{2} - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.2

Cancel the common factor of

0

$0$ and

2

$2$ .

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Step 3.2.2.2.1

Factor

2

$2$ out of

0

$0$ .

- 3 (\frac{2 (0)}{2} - \frac{{(- 1)}^{2}}{2})

$- 3 (\frac{2 (0)}{2} - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.2.2

Cancel the common factors.

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Step 3.2.2.2.2.1

Factor

2

$2$ out of

2

$2$ .

- 3 (\frac{2 \cdot 0}{2 \cdot 1} - \frac{{(- 1)}^{2}}{2})

$- 3 (\frac{2 \cdot 0}{2 \cdot 1} - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.2.2.2

Cancel the common factor.

- 3 (\frac{2 \cdot 0}{2 \cdot 1} - \frac{{(- 1)}^{2}}{2})

$- 3 (\frac{2 \cdot 0}{2 \cdot 1} - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.2.2.3

Rewrite the expression.

- 3 (\frac{0}{1} - \frac{{(- 1)}^{2}}{2})

$- 3 (\frac{0}{1} - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.2.2.4

Divide

0

$0$ by

1

$1$ .

- 3 (0 - \frac{{(- 1)}^{2}}{2})

$- 3 (0 - \frac{{(- 1)}^{2}}{2})$

- 3 (0 - \frac{{(- 1)}^{2}}{2})

$- 3 (0 - \frac{{(- 1)}^{2}}{2})$

- 3 (0 - \frac{{(- 1)}^{2}}{2})

$- 3 (0 - \frac{{(- 1)}^{2}}{2})$

Step 3.2.2.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

- 3 (0 - \frac{1}{2})

$- 3 (0 - \frac{1}{2})$

Step 3.2.2.4

Subtract

\frac{1}{2}

$\frac{1}{2}$ from

0

$0$ .

- 3 (- \frac{1}{2})

$- 3 (- \frac{1}{2})$

Step 3.2.2.5

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

3 (\frac{1}{2})

$3 (\frac{1}{2})$

Step 3.2.2.6

Combine

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{3}{2}

$\frac{3}{2}$

Decimal Form:

1.5

$1.5$

Mixed Number Form:

1 \frac{1}{2}

$1 \frac{1}{2}$

Step 5

Enter YOUR Problem

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$