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

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

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

\int_{0}^{π} e^{- x} sin (x) d x

\frac{1}{2 e ^{π}} + \frac{1}{2}

Decimal

0.52160 \dots

Solution steps

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

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

Simplify

= \frac{1}{2 e ^{π}} + \frac{1}{2}

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