Calculus Examples

$\int_{0}^{2} 3 e^{x} d x$

Step 1

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int_{0}^{2} e^{x} d x$

Step 2

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

$3 (e^{x}]_{0}^{2})$

Step 3

Substitute and simplify.

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Step 3.1

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

$3 ((e^{2}) - e^{0})$

Step 3.2

Simplify.

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Step 3.2.1

Anything raised to $0$ is $1$ .

$3 (e^{2} - 1 \cdot 1)$

Step 3.2.2

Multiply $- 1$ by $1$ .

$3 (e^{2} - 1)$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$3 e^{2} + 3 \cdot - 1$

Step 4.2

Multiply $3$ by $- 1$ .

$3 e^{2} - 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 e^{2} - 3$

Decimal Form:

$19.16716829 \dots$

Step 6