What is the integral from 2 to infinity of ye^{-3y} ?

The integral from 2 to infinity of ye^{-3y} is 7/(9e^6)

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integral from 2 to infinity of ye^{-3y}

\int_{2}^{\infty} y e^{- 3 y} d y

\frac{7}{9 e ^{6}}

Decimal

0.00192 \dots

Solution steps

\int_{2}^{\infty} y e^{- 3 y} d y

Compute the indefinite integral:

\int y e^{- 3 y} d y = \frac{1}{9} (- 3 e^{- 3 y} y - e^{- 3 y}) + C

Compute the boundaries:

\int_{2}^{\infty} y e^{- 3 y} d y = 0 - (- \frac{7}{9 e ^{6}})

= 0 - (- \frac{7}{9 e ^{6}})

Simplify

= \frac{7}{9 e ^{6}}

x \to - 2 - lim (- 2 x + 6)

\int_{0}^{1} \frac{55}{4 y - 1} d y

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What is the integral from 2 to infinity of ye^{-3y} ?
The integral from 2 to infinity of ye^{-3y} is 7/(9e^6)