What is the integral of-1/2 sin(2x) ?

The integral of-1/2 sin(2x) is 1/4 cos(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/2 sin(2x)

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

\frac{1}{4} cos (2 x) + C

Solution steps

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

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{2} \cdot \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

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

Simplify

- \frac{1}{2} \cdot \frac{1}{2} (- cos (2 x)) : \frac{1}{4} cos (2 x)

= \frac{1}{4} cos (2 x)

Add a constant to the solution

= \frac{1}{4} cos (2 x) + C

x \to 80 lim (82 - x)

\int 2 sin (π x) d x

x^{4} - 6 x^{3}

x \to - 2 - lim (2 x + 1)

\frac{d}{d x} (2 sin (8 x))

What is the integral of-1/2 sin(2x) ?
The integral of-1/2 sin(2x) is 1/4 cos(2x)+C