What is the integral from 0 to pi of 2xsin(x) ?

The integral from 0 to pi of 2xsin(x) is 2pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi of 2xsin(x)

\int_{0}^{π} 2 x sin (x) d x

2 π

Decimal

6.28318 \dots

Solution steps

\int_{0}^{π} 2 x sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

= 2 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

\int - cos (x) d x = - sin (x)

= 2 [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 2 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 2 π

What is the integral from 0 to pi of 2xsin(x) ?
The integral from 0 to pi of 2xsin(x) is 2pi