Calculus Examples

$\int_{1}^{2} e^{x} - e d x$

Step 1

Split the single integral into multiple integrals.

$\int_{1}^{2} e^{x} d x + \int_{1}^{2} - e d x$

Step 2

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

$e^{x}]_{1}^{2} + \int_{1}^{2} - e d x$

Step 3

Apply the constant rule.

$e^{x}]_{1}^{2} + - e x]_{1}^{2}$

Step 4

Simplify the answer.

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Step 4.1

Combine $e^{x}]_{1}^{2}$ and $- e x]_{1}^{2}$ .

$e^{x} - e x]_{1}^{2}$

Step 4.2

Substitute and simplify.

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Step 4.2.1

Evaluate $e^{x} - e x$ at $2$ and at $1$ .

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

Step 4.2.2

Simplify.

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Step 4.2.2.1

Multiply $2$ by $- 1$ .

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

Step 4.2.2.2

Simplify.

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

Step 4.2.2.3

Multiply $- 1$ by $1$ .

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

Step 4.2.2.4

Subtract $e$ from $e$ .

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

Step 4.2.2.5

Multiply $- 1$ by $0$ .

$e^{2} - 2 e + 0$

Step 4.2.2.6

Add $e^{2} - 2 e$ and $0$ .

$e^{2} - 2 e$

Step 5

The result can be shown in multiple forms.

Exact Form:

$e^{2} - 2 e$

Decimal Form:

$1.95249244 \dots$

Step 6