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

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

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

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

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

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- \frac{1}{e ^{3}})

Simplify

= \frac{1}{e ^{3}}

x \to 3 + lim (\frac{3}{x ^{2} - 9})

\int_{0}^{0.9} \frac{1}{1 - x} d x

8 y^{^{''}} + 2 y^{^{'}} - y = 0

sin (x), cos (x), [0, \frac{π}{2}]

\frac{d y}{d x} = 2 x e^{4 y}

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