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 Notation

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}

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

\int_{0}^{1} 2 π (x + 2) x^{2} d x

\int_{- 1}^{y - 1} \frac{3}{2} x^{2} d x

\int_{- 1}^{2} (1 - ∣ x ∣) d x

\int_{2}^{3} x^{2} + 2 d x

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