What is the integral from-1 to 1 of e^ysin(y) ?

The integral from-1 to 1 of e^ysin(y) is (-e^2cos(1)+e^2sin(1)+cos(1)+sin(1))/(2e)

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integral from-1 to 1 of e^ysin(y)

\int_{- 1}^{1} e^{y} sin (y) d y

\frac{- e ^{2} cos ( 1 ) + e ^{2} sin ( 1 ) + cos ( 1 ) + sin ( 1 )}{2 e}

Decimal

0.66349 \dots

Solution steps

\int_{- 1}^{1} e^{y} sin (y) d y

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- 1}^{1} e^{y} sin (y) d y = \frac{- e cos ( 1 ) + e sin ( 1 )}{2} - \frac{- cos ( 1 ) - sin ( 1 )}{2 e}

= \frac{- e cos ( 1 ) + e sin ( 1 )}{2} - \frac{- cos ( 1 ) - sin ( 1 )}{2 e}

Simplify

= \frac{- e ^{2} cos ( 1 ) + e ^{2} sin ( 1 ) + cos ( 1 ) + sin ( 1 )}{2 e}

What is the integral from-1 to 1 of e^ysin(y) ?
The integral from-1 to 1 of e^ysin(y) is (-e^2cos(1)+e^2sin(1)+cos(1)+sin(1))/(2e)