What is the integral from 0 to pi/4 of e^{-x}sin(x) ?

The integral from 0 to pi/4 of e^{-x}sin(x) is -1/(sqrt(2)e^{pi/4)}+1/2

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integral from 0 to pi/4 of e^{-x}sin(x)

\int_{0}^{\frac{π}{4}} e^{- x} sin (x) d x

- \frac{1}{2 e ^{\frac{π}{4}}} + \frac{1}{2}

Decimal

0.17760 \dots

Solution steps

\int_{0}^{\frac{π}{4}} e^{- x} sin (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\frac{π}{4}} e^{- x} sin (x) d x = - \frac{1}{2 e ^{\frac{π}{4}}} - (- \frac{1}{2})

= - \frac{1}{2 e ^{\frac{π}{4}}} - (- \frac{1}{2})

Simplify

= - \frac{1}{2 e ^{\frac{π}{4}}} + \frac{1}{2}

What is the integral from 0 to pi/4 of e^{-x}sin(x) ?
The integral from 0 to pi/4 of e^{-x}sin(x) is -1/(sqrt(2)e^{pi/4)}+1/2