What is the integral of cos(2pix) ?

The integral of cos(2pix) is 1/(2pi)sin(2xpi)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(2pix)

\int cos (2 π x) d x

\frac{1}{2 π} sin (2 x π) + C

Solution steps

\int cos (2 π x) d x

Apply u-substitution

: \int cos (u) \frac{1}{2 π} d u

= \int cos (u) \frac{1}{2 π} d u

Take the constant out:

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

= \frac{1}{2 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2 π} sin (u)

Substitute back

u = 2 x π

= \frac{1}{2 π} sin (2 x π)

Add a constant to the solution

= \frac{1}{2 π} sin (2 x π) + C

\frac{\partial}{\partial z} (x y sin (z))

\frac{d y}{d x} = (\frac{x}{2000}) - (\frac{y}{5000}), y (0) = 0

x \to 5 lim (- (\frac{x + 1}{x - 5}))

\int \frac{x}{5} d x

\frac{d}{d x} (\frac{5}{3 x})

What is the integral of cos(2pix) ?
The integral of cos(2pix) is 1/(2pi)sin(2xpi)+C