What is the integral of sin^2(v) ?

The integral of sin^2(v) is 1/2 (v-1/2 sin(2v))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin^2(v)

\int sin^{2} (v) d v

\frac{1}{2} (v - \frac{1}{2} sin (2 v)) + C

Solution steps

\int sin^{2} (v) d v

Rewrite using trig identities

= \int \frac{1 - cos ( 2 v )}{2} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 - cos (2 v) d v

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d v - \int cos (2 v) d v)

\int 1 d v = v

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

= \frac{1}{2} (v - \frac{1}{2} sin (2 v))

Add a constant to the solution

= \frac{1}{2} (v - \frac{1}{2} sin (2 v)) + C

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