Calculus Examples

$\int_{- 1}^{1} x^{100} d x$

Step 1

By the Power Rule, the integral of $x^{100}$ with respect to $x$ is $\frac{1}{101} x^{101}$ .

$\frac{1}{101} x^{101}]_{- 1}^{1}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $\frac{1}{101} x^{101}$ at $1$ and at $- 1$ .

$(\frac{1}{101} \cdot 1^{101}) - \frac{1}{101} {(- 1)}^{101}$

Step 2.2

Simplify.

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Step 2.2.1

One to any power is one.

$\frac{1}{101} \cdot 1 - \frac{1}{101} {(- 1)}^{101}$

Step 2.2.2

Multiply $\frac{1}{101}$ by $1$ .

$\frac{1}{101} - \frac{1}{101} {(- 1)}^{101}$

Step 2.2.3

Raise $- 1$ to the power of $101$ .

$\frac{1}{101} - \frac{1}{101} \cdot - 1$

Step 2.2.4

Multiply $- 1$ by $- 1$ .

$\frac{1}{101} + 1 (\frac{1}{101})$

Step 2.2.5

Multiply $\frac{1}{101}$ by $1$ .

$\frac{1}{101} + \frac{1}{101}$

Step 2.2.6

Combine the numerators over the common denominator.

$\frac{1 + 1}{101}$

Step 2.2.7

Add $1$ and $1$ .

$\frac{2}{101}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{101}$

Decimal Form:

$0.\overline{0198}$

Step 4