What is the integral from 0 to pi/6 of xsin(x+y) ?

The integral from 0 to pi/6 of xsin(x+y) is -pi/6 cos(y+pi/6)+sin(y+pi/6)-sin(y)

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/6 of xsin(x+y)

\int_{0}^{\frac{π}{6}} x sin (x + y) d x

- \frac{π}{6} cos (y + \frac{π}{6}) + sin (y + \frac{π}{6}) - sin (y)

Solution steps

\int_{0}^{\frac{π}{6}} x sin (x + y) d x

Apply Integration By Parts

: [- x cos (y + x) - \int - cos (y + x) d x]_{0}^{\frac{π}{6}}

= [- x cos (y + x) - \int - cos (y + x) d x]_{0}^{\frac{π}{6}}

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

= [- x cos (y + x) - (- sin (y + x))]_{0}^{\frac{π}{6}}

Simplify

= [- x cos (y + x) + sin (y + x)]_{0}^{\frac{π}{6}}

Compute the boundaries:

- \frac{π}{6} cos (y + \frac{π}{6}) + sin (y + \frac{π}{6}) - sin (y)

= - \frac{π}{6} cos (y + \frac{π}{6}) + sin (y + \frac{π}{6}) - sin (y)

\frac{d}{d x} (ln (1 + 10 x))

x \to 4 + lim (2 x)

x \to 0 + lim (cot (x))

\int_{0}^{2} (2 x + 5) d x

What is the integral from 0 to pi/6 of xsin(x+y) ?
The integral from 0 to pi/6 of xsin(x+y) is -pi/6 cos(y+pi/6)+sin(y+pi/6)-sin(y)