What is the integral from 0 to pi/4 of e^xcos(x) ?

The integral from 0 to pi/4 of e^xcos(x) is (e^{pi/4})/(sqrt(2))-1/2

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integral from 0 to pi/4 of e^xcos(x)

\int_{0}^{\frac{π}{4}} e^{x} cos (x) d x

\frac{e ^{\frac{π}{4}}}{2} - \frac{1}{2}

Decimal

1.05088 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 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}^{\frac{π}{4}} e^{x} cos (x) d x = \frac{e ^{\frac{π}{4}}}{2} - \frac{1}{2}

= \frac{e ^{\frac{π}{4}}}{2} - \frac{1}{2}

What is the integral from 0 to pi/4 of e^xcos(x) ?
The integral from 0 to pi/4 of e^xcos(x) is (e^{pi/4})/(sqrt(2))-1/2