What is the integral of sin(kt) ?

The integral of sin(kt) is -1/k cos(kt)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin(kt)

\int sin (k t) d t

- \frac{1}{k} cos (k t) + C

Solution steps

\int sin (k t) d t

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = k t

= \frac{1}{k} (- cos (k t))

Simplify

= - \frac{1}{k} cos (k t)

Add a constant to the solution

= - \frac{1}{k} cos (k t) + C