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

The integral of sin(x/2)cos(x/2) is -1/2 cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x/2)cos(x/2)

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

- \frac{1}{2} cos (x) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{2} sin (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (x) d x

Use the common integral:

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

= \frac{1}{2} (- cos (x))

Simplify

= - \frac{1}{2} cos (x)

Add a constant to the solution

= - \frac{1}{2} cos (x) + C

\frac{\partial}{\partial y} (4 z)

f (x) = 1 - \frac{49}{x ^{2}}

\int x^{- 11} d x

\int \frac{2}{4 x ^{3}} d x

f (x) = \frac{3 x}{x + 1}, (2, 2)

What is the integral of sin(x/2)cos(x/2) ?
The integral of sin(x/2)cos(x/2) is -1/2 cos(x)+C