What is the integral from pi/4 to pi of |cos(x)| ?

The integral from pi/4 to pi of |cos(x)| is -1/(sqrt(2))+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from pi/4 to pi of |cos(x)|

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

- \frac{1}{2} + 2

Decimal Notation

1.29289 \dots

Solution steps

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

Eliminate Absolutes

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

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

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

= 1 - \frac{1}{2} + 1

Simplify

= - \frac{1}{2} + 2

\int_{0}^{1} (2 t + 1) e^{- s t} d t

\int_{0}^{3} 0 d x

\int_{0}^{15 π} sin (x) d x

\int_{0}^{3} 5^{2 x} d x

\int_{0}^{1} x \cdot e^{2 x} d x

What is the integral from pi/4 to pi of |cos(x)| ?
The integral from pi/4 to pi of |cos(x)| is -1/(sqrt(2))+2