What is the integral from 0 to pi of e^xcos(x) ?

The integral from 0 to pi of e^xcos(x) is (-e^pi-1)/2

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integral from 0 to pi of e^xcos(x)

\int_{0}^{π} e^{x} cos (x) d x

\frac{- e ^{π} - 1}{2}

Decimal Notation

- 12.07034 \dots

Solution steps

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

= - \frac{e ^{π}}{2} - \frac{1}{2}

Simplify

= \frac{- e ^{π} - 1}{2}

n = 0 \sum \infty \frac{5}{3 ^{n - 1}}

x^{\frac{1}{5}}, x^{\frac{1}{2}}

x^{^{'}} + x = 0, x (0) = 1

n = 2 \sum \infty \frac{1}{n \cdot ln ( n )}

\int_{0}^{\frac{π}{2}} (sin^{2} (x)) d x

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