What is the integral from 1 to infinity of 3e^{-x} ?

The integral from 1 to infinity of 3e^{-x} is 3/e

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integral from 1 to infinity of 3e^{-x}

\int_{1}^{\infty} 3 e^{- x} d x

\frac{3}{e}

Decimal

1.10363 \dots

Solution steps

\int_{1}^{\infty} 3 e^{- x} d x

Compute the indefinite integral:

\int 3 e^{- x} d x = - 3 e^{- x} + C

Compute the boundaries:

\int_{1}^{\infty} 3 e^{- x} d x = 0 - (- \frac{3}{e})

= 0 - (- \frac{3}{e})

Simplify

= \frac{3}{e}

What is the integral from 1 to infinity of 3e^{-x} ?
The integral from 1 to infinity of 3e^{-x} is 3/e