What is the integral from 0 to infinity of e^{-x/4} ?

The integral from 0 to infinity of e^{-x/4} is 4

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integral from 0 to infinity of e^{-x/4}

\int_{0}^{\infty} e^{- \frac{x}{4}} d x

4

Solution steps

\int_{0}^{\infty} e^{- \frac{x}{4}} d x

Compute the indefinite integral:

\int e^{- \frac{x}{4}} d x = - 4 e^{- \frac{x}{4}} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- \frac{x}{4}} d x = 0 - (- 4)

= 0 - (- 4)

Simplify

= 4

x \to 0 lim ((1 + x)^{\frac{2}{x}})

\frac{d}{d x} (4 e^{3 x} + 12 x e^{3 x})

sin (5 t)

\frac{\partial}{\partial x} (- 3 x y (- 3 - x - y))

What is the integral from 0 to infinity of e^{-x/4} ?
The integral from 0 to infinity of e^{-x/4} is 4