Calculus Examples

$\int_{0}^{2} e^{x} d x$

Step 1

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

$e^{x}]_{0}^{2}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $e^{x}$ at $2$ and at $0$ .

$(e^{2}) - e^{0}$

Step 2.2

Simplify.

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Step 2.2.1

Anything raised to $0$ is $1$ .

$e^{2} - 1 \cdot 1$

Step 2.2.2

Multiply $- 1$ by $1$ .

$e^{2} - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$e^{2} - 1$

Decimal Form:

$6.38905609 \dots$

Step 4