Calculus Examples

$\int_{0}^{1} e^{x} - 2 d x$

Step 1

Split the single integral into multiple integrals.

$\int_{0}^{1} e^{x} d x + \int_{0}^{1} - 2 d x$

Step 2

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

$e^{x}]_{0}^{1} + \int_{0}^{1} - 2 d x$

Step 3

Apply the constant rule.

$e^{x}]_{0}^{1} + - 2 x]_{0}^{1}$

Step 4

Simplify the answer.

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Step 4.1

Combine $e^{x}]_{0}^{1}$ and $- 2 x]_{0}^{1}$ .

$e^{x} - 2 x]_{0}^{1}$

Step 4.2

Substitute and simplify.

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Step 4.2.1

Evaluate $e^{x} - 2 x$ at $1$ and at $0$ .

$(e^{1} - 2 \cdot 1) - (e^{0} - 2 \cdot 0)$

Step 4.2.2

Simplify.

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Step 4.2.2.1

Simplify.

$e - 2 \cdot 1 - (e^{0} - 2 \cdot 0)$

Step 4.2.2.2

Multiply $- 2$ by $1$ .

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

Step 4.2.2.3

Anything raised to $0$ is $1$ .

$e - 2 - (1 - 2 \cdot 0)$

Step 4.2.2.4

Multiply $- 2$ by $0$ .

$e - 2 - (1 + 0)$

Step 4.2.2.5

Add $1$ and $0$ .

$e - 2 - 1 \cdot 1$

Step 4.2.2.6

Multiply $- 1$ by $1$ .

$e - 2 - 1$

Step 4.2.2.7

Subtract $1$ from $- 2$ .

$e - 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$e - 3$

Decimal Form:

$- 0.28171817 \dots$

Step 6