What is the integral from 0 to infinity of ((ye^{-y/a}))/a ?

The integral from 0 to infinity of ((ye^{-y/a}))/a is a

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integral from 0 to infinity of ((ye^{-y/a}))/a

\int_{0}^{\infty} \frac{( y e ^{- \frac{y}{a}} )}{a} d y

a

Solution steps

\int_{0}^{\infty} \frac{y e ^{- \frac{y}{a}}}{a} d y

Compute the indefinite integral:

\int \frac{y e ^{- \frac{y}{a}}}{a} d y = - e^{- \frac{y}{a}} (y + a) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{( y e ^{- \frac{y}{a}} )}{a} d y = 0 - (- a)

= 0 - (- a)

Simplify

= a

What is the integral from 0 to infinity of ((ye^{-y/a}))/a ?
The integral from 0 to infinity of ((ye^{-y/a}))/a is a