What is the integral from 0 to infinity of pie^{-2x} ?

The integral from 0 to infinity of pie^{-2x} is pi/2

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integral from 0 to infinity of pie^{-2x}

\int_{0}^{\infty} π e^{- 2 x} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{\infty} π e^{- 2 x} d x

Compute the indefinite integral:

\int π e^{- 2 x} d x = - \frac{π}{2} e^{- 2 x} + C

Compute the boundaries:

\int_{0}^{\infty} π e^{- 2 x} d x = 0 - (- \frac{π}{2})

= 0 - (- \frac{π}{2})

Simplify

= \frac{π}{2}

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What is the integral from 0 to infinity of pie^{-2x} ?
The integral from 0 to infinity of pie^{-2x} is pi/2