Calculus Examples

$\int_{0}^{b} 5 e^{x} d x$

Step 1

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int_{0}^{b} e^{x} d x$

Step 2

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

$5 (e^{x}]_{0}^{b})$

Step 3

Substitute and simplify.

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Step 3.1

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

$5 ((e^{b}) - e^{0})$

Step 3.2

Simplify.

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Step 3.2.1

Anything raised to $0$ is $1$ .

$5 (e^{b} - 1 \cdot 1)$

Step 3.2.2

Multiply $- 1$ by $1$ .

$5 (e^{b} - 1)$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$5 e^{b} + 5 \cdot - 1$

Step 4.2

Multiply $5$ by $- 1$ .

$5 e^{b} - 5$