What is the integral from 0 to infinity of 2ye^{-2y} ?

The integral from 0 to infinity of 2ye^{-2y} is 1/2

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integral from 0 to infinity of 2ye^{-2y}

\int_{0}^{\infty} 2 y e^{- 2 y} d y

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\infty} 2 y e^{- 2 y} d y

Compute the indefinite integral:

\int 2 y e^{- 2 y} d y = - e^{- 2 y} y - \frac{1}{2} e^{- 2 y} + C

Compute the boundaries:

\int_{0}^{\infty} 2 y e^{- 2 y} d y = 0 - (- \frac{1}{2})

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

What is the integral from 0 to infinity of 2ye^{-2y} ?
The integral from 0 to infinity of 2ye^{-2y} is 1/2