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

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

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 xcos(x/3)

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

\frac{3 π}{4} + \frac{9 3}{2} - 9

Decimal Notation

1.15042 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

\frac{3 π}{4} + 9 \cdot \frac{3}{2} - 9

= \frac{3 π}{4} + 9 \cdot \frac{3}{2} - 9

Simplify

= \frac{3 π}{4} + \frac{9 3}{2} - 9

\frac{2 ln ( x )}{x}

\frac{d y}{d x} = 2 y (9 - y)

\frac{d x}{d t} = x (1 - \frac{1}{2500} x)

\int (x + 4) 8 x + x^{2} d x

\frac{d}{d x} (r^{2} - 7 x^{2})

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