What is the integral from 0 to infinity of t*e^{-t} ?

The integral from 0 to infinity of t*e^{-t} is 1

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integral from 0 to infinity of t*e^{-t}

\int_{0}^{\infty} t \cdot e^{- t} d t

1

Solution steps

\int_{0}^{\infty} t e^{- t} d t

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

f (x) = cos (sin^{2} (x))

\int π^{2} r^{4} d r

f (x) = 2 x + 3 x

\frac{d}{d x} (tan (e^{x}) + e^{t a n (x)})

y = x^{2} + 5 x + 9

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