What is the integral from 0 to infinity of 2e^{-x}sin(x) ?

The integral from 0 to infinity of 2e^{-x}sin(x) is 1

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integral from 0 to infinity of 2e^{-x}sin(x)

\int_{0}^{\infty} 2 e^{- x} sin (x) d x

1

Solution steps

\int_{0}^{\infty} 2 e^{- x} sin (x) d x

Compute the indefinite integral:

\int 2 e^{- x} sin (x) d x = - e^{- x} cos (x) - e^{- x} sin (x) + C

Compute the boundaries:

\int_{0}^{\infty} 2 e^{- x} sin (x) d x = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

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What is the integral from 0 to infinity of 2e^{-x}sin(x) ?
The integral from 0 to infinity of 2e^{-x}sin(x) is 1