What is the integral of sin(wx) ?

The integral of sin(wx) is -1/w cos(wx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(wx)

\int sin (w x) d x

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

Solution steps

\int sin (w x) d x

Apply u-substitution

: \int \frac{sin ( u )}{w} d u

= \int \frac{sin ( u )}{w} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{w} (- cos (u))

Substitute back

u = w x

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

Simplify

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

Add a constant to the solution

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

f (x) = 9 x^{3}

z \to 0 lim (\frac{sin ( z )}{z})

\int 2 + x d x

x \to 1 lim (a x^{2} + b x + c)

x \to + 0 + lim (\frac{1}{x ^{\frac{2}{3}}})