What is the integral of (sin(x/2)) ?

The integral of (sin(x/2)) is -2cos(x/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sin(x/2))

\int (sin (\frac{x}{2})) d x

- 2 cos (\frac{x}{2}) + C

Solution steps

\int sin (\frac{x}{2}) d x

Apply u-substitution

= \int sin (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = \frac{x}{2}

= 2 (- cos (\frac{x}{2}))

Simplify

= - 2 cos (\frac{x}{2})

Add a constant to the solution

= - 2 cos (\frac{x}{2}) + C