What is the integral from 0 to pi/2 of xsin(x/3) ?

The integral from 0 to pi/2 of xsin(x/3) is 9/2-(3sqrt(3)pi)/4

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 xsin(x/3)

\int_{0}^{\frac{π}{2}} x sin (\frac{x}{3}) d x

\frac{9}{2} - \frac{3 3 π}{4}

Decimal Notation

0.41895 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x sin (\frac{x}{3}) d x

Apply Integration By Parts

: [- 3 x cos (\frac{x}{3}) - \int - 3 cos (\frac{x}{3}) d x]_{0}^{\frac{π}{2}}

= [- 3 x cos (\frac{x}{3}) - \int - 3 cos (\frac{x}{3}) d x]_{0}^{\frac{π}{2}}

\int - 3 cos (\frac{x}{3}) d x = - 9 sin (\frac{x}{3})

= [- 3 x cos (\frac{x}{3}) - (- 9 sin (\frac{x}{3}))]_{0}^{\frac{π}{2}}

Simplify

= [- 3 x cos (\frac{x}{3}) + 9 sin (\frac{x}{3})]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{9}{2} - \frac{3 3 π}{4}

= \frac{9}{2} - \frac{3 3 π}{4}

\frac{\partial}{\partial s} (- 2 s^{2} + t^{2})

\frac{\partial}{\partial x} (x - 2 y)

\frac{d}{d x} (5 arcsin (x^{4}))

\int 23 e^{39 x} d x

\frac{8}{8 x + 9}

What is the integral from 0 to pi/2 of xsin(x/3) ?
The integral from 0 to pi/2 of xsin(x/3) is 9/2-(3sqrt(3)pi)/4