What is the integral from pi/6 to pi of |cos(x)| ?

The integral from pi/6 to pi of |cos(x)| is 3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from pi/6 to pi of |cos(x)|

\int_{\frac{π}{6}}^{π} ∣ cos (x) ∣ d x

\frac{3}{2}

Solution steps

\int_{\frac{π}{6}}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

= \int_{\frac{π}{6}}^{\frac{π}{2}} cos (x) d x + \int_{\frac{π}{2}}^{π} - cos (x) d x

\int_{\frac{π}{6}}^{\frac{π}{2}} cos (x) d x = \frac{1}{2}

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

= \frac{1}{2} + 1

Simplify

\frac{1}{2} + 1 : \frac{3}{2}

= \frac{3}{2}

\int_{1}^{3} (3 x + 1) d x

\int_{0}^{4} (2 t^{2} + t^{\frac{3}{2}}) d t

\int_{0}^{1} 1 + 6 x^{\frac{3}{2}} d x

\int_{0}^{25} 2 x d x

\int_{0}^{2} (\frac{x ^{2} - 2}{x + 1}) d x

What is the integral from pi/6 to pi of |cos(x)| ?
The integral from pi/6 to pi of |cos(x)| is 3/2