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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi/4 of e^tcos(t)

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

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

Decimal Notation

1.05088 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{t} cos (t) d t = \frac{e ^{t} sin ( t )}{2} + \frac{e ^{t} cos ( t )}{2} + C

Compute the boundaries:

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

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

\int_{0}^{2} (x^{3} + x^{2} + x) d x

\int_{0}^{1} \frac{x ^{15}}{x ^{8} + 1} d x

\int_{0}^{1} (1 - x^{4})^{7} d x

\int_{1}^{4} (2 x - 1)^{5} d x

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

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