Calculus Examples

$\int_{0}^{\ln (2)} e^{x} d x$

Step 1

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

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

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $e^{x}$ at $\ln (2)$ and at $0$ .

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

Step 2.2

Simplify.

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Step 2.2.1

Exponentiation and log are inverse functions.

$2 - e^{0}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$2 - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$2 - 1$

Step 2.2.4

Subtract $1$ from $2$ .

$1$

Step 3