What is the integral of 1/2 sin(2θ) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/2 sin(2θ)

\int \frac{1}{2} sin (2 θ) d θ

- \frac{1}{4} cos (2 θ) + C

Solution steps

\int \frac{1}{2} sin (2 θ) d θ

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 θ) d θ

Apply u-substitution

= \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 θ

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

Simplify

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

= - \frac{1}{4} cos (2 θ)

Add a constant to the solution

= - \frac{1}{4} cos (2 θ) + C

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