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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/2 of e^xcos(x)

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

\frac{e ^{\frac{π}{2}} - 1}{2}

Decimal

1.90523 \dots

Solution steps

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

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

Simplify

= \frac{e ^{\frac{π}{2}} - 1}{2}

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