What is the integral from-3 to 4 of e^{x+7} ?

The integral from-3 to 4 of e^{x+7} is e^{11}-e^4

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integral from-3 to 4 of e^{x+7}

\int_{- 3}^{4} e^{x + 7} d x

e^{11} - e^{4}

Decimal

59819.54356 \dots

Solution steps

\int_{- 3}^{4} e^{x + 7} d x

e^{x + 7} = e^{7} e^{x}

= \int_{- 3}^{4} e^{7} e^{x} d x

Take the constant out:

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

= e^{7} \cdot \int_{- 3}^{4} e^{x} d x

Use the common integral:

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

= e^{7} [e^{x}]_{- 3}^{4}

Compute the boundaries:

e^{4} - \frac{1}{e ^{3}}

= e^{7} (e^{4} - \frac{1}{e ^{3}})

Simplify

= e^{11} - e^{4}

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What is the integral from-3 to 4 of e^{x+7} ?
The integral from-3 to 4 of e^{x+7} is e^{11}-e^4