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

The integral from 0 to infinity of 4e^{-4x} is 1

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

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

1

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} 4 e^{- 4 x} d x = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

\int \frac{x}{x - 2} d x

x \to - 2 lim (\frac{5 x ^{2} + 6 x - 8}{x + 2})

\frac{d}{d x} ((x^{2} - 9)^{2})

\frac{\partial}{\partial x} (\frac{- 5 x - y}{y ^{2} + x ^{2}})

\frac{8}{s ^{4}}

What is the integral from 0 to infinity of 4e^{-4x} ?
The integral from 0 to infinity of 4e^{-4x} is 1