What is the integral of-cos((nxpi)/2) ?

The integral of-cos((nxpi)/2) is -2/(pin)sin((nxpi)/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-cos((nxpi)/2)

\int - cos (\frac{n x π}{2}) d x

- \frac{2}{πn} sin (\frac{n x π}{2}) + C

Solution steps

\int - cos (\frac{n x π}{2}) d x

Take the constant out:

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

= - \int cos (\frac{n x π}{2}) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{πn} d u

= - \int \frac{2 cos ( u )}{πn} d u

Take the constant out:

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

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

Use the common integral:

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

= - \frac{2}{πn} sin (u)

Substitute back

u = \frac{n x π}{2}

= - \frac{2}{πn} sin (\frac{n x π}{2})

Add a constant to the solution

= - \frac{2}{πn} sin (\frac{n x π}{2}) + C

(4 - t) (2 + t^{2})^{- 1}

x y^{^{'}} + y = x^{2} y^{2}

\int \frac{x + 5}{3 x + 9} d x

\int \frac{1}{2} (1 - cos (θ))^{2} d θ

\int (x^{2} - 6 x + 2) \cdot e^{x} d x

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