What is the integral from-2 to 3 of e^{x+2} ?

The integral from-2 to 3 of e^{x+2} is e^5-1

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integral from-2 to 3 of e^{x+2}

\int_{- 2}^{3} e^{x + 2} d x

e^{5} - 1

Decimal

147.41315 \dots

Solution steps

\int_{- 2}^{3} e^{x + 2} d x

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

= \int_{- 2}^{3} 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}^{3} e^{x} d x

Use the common integral:

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

= e^{2} [e^{x}]_{- 2}^{3}

Compute the boundaries:

e^{3} - \frac{1}{e ^{2}}

= e^{2} (e^{3} - \frac{1}{e ^{2}})

Simplify

= e^{5} - 1

What is the integral from-2 to 3 of e^{x+2} ?
The integral from-2 to 3 of e^{x+2} is e^5-1