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

The integral from 0 to pi/2 of e^{-x}sin(2x) is 2/(5e^{pi/2)}+2/5

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

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

\frac{2}{5 e ^{\frac{π}{2}}} + \frac{2}{5}

Decimal

0.48315 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{- x} sin (2 x) d x = - \frac{2 e ^{- x} cos ( 2 x )}{5} - \frac{e ^{- x} sin ( 2 x )}{5} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- x} sin (2 x) d x = \frac{2}{5 e ^{\frac{π}{2}}} - (- \frac{2}{5})

= \frac{2}{5 e ^{\frac{π}{2}}} - (- \frac{2}{5})

Simplify

= \frac{2}{5 e ^{\frac{π}{2}}} + \frac{2}{5}

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What is the integral from 0 to pi/2 of e^{-x}sin(2x) ?
The integral from 0 to pi/2 of e^{-x}sin(2x) is 2/(5e^{pi/2)}+2/5