What is the integral from-2 to 1 of e^{u+2} ?

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

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integral from-2 to 1 of e^{u+2}

\int_{- 2}^{1} e^{u + 2} d u

e^{3} - 1

Decimal

19.08553 \dots

Solution steps

\int_{- 2}^{1} e^{u + 2} d u

e^{u + 2} = e^{2} e^{u}

= \int_{- 2}^{1} e^{2} e^{u} d u

Take the constant out:

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

= e^{2} \cdot \int_{- 2}^{1} e^{u} d u

Use the common integral:

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

= e^{2} [e^{u}]_{- 2}^{1}

Compute the boundaries:

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

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

Simplify

= e^{3} - 1

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