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

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

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

\int_{- π}^{π} e^{x} cos (x) d x

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

Decimal Notation

- 11.54873 \dots

Solution steps

\int_{- π}^{π} e^{x} cos (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

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