What is the integral from 0 to 7 of e^{x-7} ?

The integral from 0 to 7 of e^{x-7} is (e^7-1)/(e^7)

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integral from 0 to 7 of e^{x-7}

\int_{0}^{7} e^{x - 7} d x

\frac{e ^{7} - 1}{e ^{7}}

Decimal Notation

0.99908 \dots

Solution steps

\int_{0}^{7} e^{x - 7} d x

e^{x - 7} = e^{- 7} e^{x}

= \int_{0}^{7} 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_{0}^{7} e^{x} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{7}} \cdot \int_{0}^{7} e^{x} d x

Use the common integral:

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

= \frac{1}{e ^{7}} [e^{x}]_{0}^{7}

Compute the boundaries:

e^{7} - 1

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

Simplify

= \frac{e ^{7} - 1}{e ^{7}}

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What is the integral from 0 to 7 of e^{x-7} ?
The integral from 0 to 7 of e^{x-7} is (e^7-1)/(e^7)