What is the integral of sin(10w) ?

The integral of sin(10w) is -1/10 cos(10w)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(10w)

\int sin (10 w) d w

- \frac{1}{10} cos (10 w) + C

Solution steps

\int sin (10 w) d w

Apply u-substitution

: \int sin (u) \frac{1}{10} d u

= \int sin (u) \frac{1}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{10} (- cos (u))

Substitute back

u = 10 w

= \frac{1}{10} (- cos (10 w))

Simplify

= - \frac{1}{10} cos (10 w)

Add a constant to the solution

= - \frac{1}{10} cos (10 w) + C

\int \frac{1}{( x ^{2} + a ^{2} )} d x

\int \frac{1}{x cos ( 1 - x )} d x

\int \frac{x ^{7}}{x ^{4} + 1} d x

\int x cos (2 x) sin (2 x) d x

\int \frac{5}{e ^{t}} d t