Calculus Examples

$\int_{0}^{1} - 2 x d x$

Step 1

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

$- 2 \int_{0}^{1} x d x$

Step 2

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

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

Step 3

Simplify the answer.

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

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

Substitute and simplify.

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Evaluate $\frac{x^{2}}{2}$ at $1$ and at $0$ .

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

Simplify.

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One to any power is one.

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

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

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

Cancel the common factor of $0$ and $2$ .

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Factor $2$ out of $0$ .

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

Cancel the common factors.

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Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $0$ by $1$ .

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

Multiply $- 1$ by $0$ .

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

Add $\frac{1}{2}$ and $0$ .

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

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

$\frac{- 2}{2}$

Cancel the common factor of $- 2$ and $2$ .

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Factor $2$ out of $- 2$ .

$\frac{2 \cdot - 1}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

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

Cancel the common factor.

$\frac{2 \cdot - 1}{2 \cdot 1}$

Rewrite the expression.

$\frac{- 1}{1}$

Divide $- 1$ by $1$ .

$- 1$

Step 4

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