Calculus Examples

$\int_{- 1}^{1} x^{299} d x$

Step 1

By the Power Rule, the integral of $x^{299}$ with respect to $x$ is $\frac{1}{300} x^{300}$ .

$\frac{1}{300} x^{300}]_{- 1}^{1}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $\frac{1}{300} x^{300}$ at $1$ and at $- 1$ .

$(\frac{1}{300} \cdot 1^{300}) - \frac{1}{300} {(- 1)}^{300}$

Step 2.2

Simplify.

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Step 2.2.1

One to any power is one.

$\frac{1}{300} \cdot 1 - \frac{1}{300} {(- 1)}^{300}$

Step 2.2.2

Multiply $\frac{1}{300}$ by $1$ .

$\frac{1}{300} - \frac{1}{300} {(- 1)}^{300}$

Step 2.2.3

Raise $- 1$ to the power of $300$ .

$\frac{1}{300} - \frac{1}{300} \cdot 1$

Step 2.2.4

Multiply $- 1$ by $1$ .

$\frac{1}{300} - \frac{1}{300}$

Step 2.2.5

Combine the numerators over the common denominator.

$\frac{1 - 1}{300}$

Step 2.2.6

Subtract $1$ from $1$ .

$\frac{0}{300}$

Step 2.2.7

Cancel the common factor of $0$ and $300$ .

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Step 2.2.7.1

Factor $300$ out of $0$ .

$\frac{300 (0)}{300}$

Step 2.2.7.2

Cancel the common factors.

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Step 2.2.7.2.1

Factor $300$ out of $300$ .

$\frac{300 \cdot 0}{300 \cdot 1}$

Step 2.2.7.2.2

Cancel the common factor.

$\frac{300 \cdot 0}{300 \cdot 1}$

Step 2.2.7.2.3

Rewrite the expression.

$\frac{0}{1}$

Step 2.2.7.2.4

Divide $0$ by $1$ .

$0$

Step 3