Calculus Examples

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

Step 1

The integral of $e^{x}$ with respect to $x$ is $e^{x}$ .

$e^{x}]_{- 1}^{1}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $e^{x}$ at $1$ and at $- 1$ .

$(e^{1}) - e^{- 1}$

Step 2.2

Simplify.

$e - e^{- 1}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$e - \frac{1}{e}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e - \frac{1}{e}$

Decimal Form:

$2.35040238 \dots$

Step 5