What is the integral from 1 to infinity of 7e^{-7x} ?

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

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integral from 1 to infinity of 7e^{-7x}

\int_{1}^{\infty} 7 e^{- 7 x} d x

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

Decimal

0.00091 \dots

Solution steps

\int_{1}^{\infty} 7 e^{- 7 x} d x

Compute the indefinite integral:

\int 7 e^{- 7 x} d x = - e^{- 7 x} + C

Compute the boundaries:

\int_{1}^{\infty} 7 e^{- 7 x} d x = 0 - (- \frac{1}{e ^{7}})

= 0 - (- \frac{1}{e ^{7}})

Simplify

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

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