What is the integral from-2 to 2 of (e^{x+2}) ?

The integral from-2 to 2 of (e^{x+2}) is e^4-1

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integral from-2 to 2 of (e^{x+2})

\int_{- 2}^{2} (e^{x + 2}) d x

e^{4} - 1

Decimal

53.59815 \dots

Solution steps

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

e^{x + 2} = e^{2} e^{x}

= \int_{- 2}^{2} e^{2} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int_{- 2}^{2} e^{x} d x

Use the common integral:

\int e^{x} d x = e^{x}

= e^{2} [e^{x}]_{- 2}^{2}

Compute the boundaries:

e^{2} - \frac{1}{e ^{2}}

= e^{2} (e^{2} - \frac{1}{e ^{2}})

Simplify

= e^{4} - 1

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What is the integral from-2 to 2 of (e^{x+2}) ?
The integral from-2 to 2 of (e^{x+2}) is e^4-1