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

The integral from 0 to t of e^xcos(x) is (e^tsin(t)+e^tcos(t)-1)/2

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

\int_{0}^{t} e^{x} cos (x) d x

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

Solution steps

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

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

Simplify

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

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