What is the integral of cos(2pinx) ?

The integral of cos(2pinx) is 1/(2pin)sin(2pinx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(2pinx)

\int cos (2 πn x) d x

\frac{1}{2 πn} sin (2 πn x) + C

Solution steps

\int cos (2 πn x) d x

Apply u-substitution

: \int \frac{cos ( u )}{2 πn} d u

= \int \frac{cos ( u )}{2 πn} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2 πn} sin (u)

Substitute back

u = 2 πn x

= \frac{1}{2 πn} sin (2 πn x)

Add a constant to the solution

= \frac{1}{2 πn} sin (2 πn x) + C

n = 0 \sum \infty \frac{( x - 3 ) ^{n}}{n}

\frac{d}{d x} (\frac{1}{e ^{\frac{1}{x}}})

\frac{d}{d x} (2 x - 9)

x \to 0 lim (4^{x})

\frac{s - 5}{( s ^{2} - 6 s + 25 )}

What is the integral of cos(2pinx) ?
The integral of cos(2pinx) is 1/(2pin)sin(2pinx)+C