What is the integral from 0 to pi/2 of (x-sin(x)) ?

The integral from 0 to pi/2 of (x-sin(x)) is (pi^2)/8-1

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/2 of (x-sin(x))

\int_{0}^{\frac{π}{2}} (x - sin (x)) d x

\frac{π ^{2}}{8} - 1

Decimal Notation

0.23370 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x - sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{2}} x d x - \int_{0}^{\frac{π}{2}} sin (x) d x

\int_{0}^{\frac{π}{2}} x d x = \frac{π ^{2}}{8}

\int_{0}^{\frac{π}{2}} sin (x) d x = 1

= \frac{π ^{2}}{8} - 1

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

\int_{- 2}^{4} 1 - x - 4 x^{3} + 2 x^{5} d x

\int_{0}^{y} x (y^{2} - x^{2})^{\frac{3}{2}} d x

\int_{0}^{\frac{π}{2}} 4 sin (\frac{x}{2}) d x

\int_{0}^{2 π} 4 cos^{2} (x) d x

What is the integral from 0 to pi/2 of (x-sin(x)) ?
The integral from 0 to pi/2 of (x-sin(x)) is (pi^2)/8-1