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

The integral from pi/2 to pi of sin(x)-x is 1-(3pi^2)/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from pi/2 to pi of sin(x)-x

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

1 - \frac{3 π ^{2}}{8}

Decimal

- 2.70110 \dots

Solution steps

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

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

\int_{\frac{π}{2}}^{π} x d x = \frac{3 π ^{2}}{8}

= 1 - \frac{3 π ^{2}}{8}

What is the integral from pi/2 to pi of sin(x)-x ?
The integral from pi/2 to pi of sin(x)-x is 1-(3pi^2)/8