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

The integral from 0 to pi/2 of e^{-5x}sin(x) is -5/(26e^{\frac{5pi){2}}}+1/26

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

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

- \frac{5}{26 e ^{\frac{5 π}{2}}} + \frac{1}{26}

Solution steps

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

Compute the indefinite integral:

\int e^{- 5 x} sin (x) d x = - \frac{e ^{- 5 x} cos ( x )}{26} - \frac{5 e ^{- 5 x} sin ( x )}{26} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- 5 x} sin (x) d x = - \frac{5}{26 e ^{\frac{5 π}{2}}} - (- \frac{1}{26})

= - \frac{5}{26 e ^{\frac{5 π}{2}}} - (- \frac{1}{26})

Simplify

= - \frac{5}{26 e ^{\frac{5 π}{2}}} + \frac{1}{26}

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What is the integral from 0 to pi/2 of e^{-5x}sin(x) ?
The integral from 0 to pi/2 of e^{-5x}sin(x) is -5/(26e^{\frac{5pi){2}}}+1/26