What is the integral from-pi to pi of e^xsin(x) ?

The integral from-pi to pi of e^xsin(x) is (e^pi)/2-1/(2e^pi)

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integral from-pi to pi of e^xsin(x)

\int_{- π}^{π} e^{x} sin (x) d x

\frac{e ^{π}}{2} - \frac{1}{2 e ^{π}}

Decimal

11.54873 \dots

Solution steps

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

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

What is the integral from-pi to pi of e^xsin(x) ?
The integral from-pi to pi of e^xsin(x) is (e^pi)/2-1/(2e^pi)