What is the integral of cos(npi x/2) ?

The integral of cos(npi x/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

integral of cos(npi x/2)

\int cos (nπ \frac{x}{2}) d x

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

Solution steps

\int cos (nπ \frac{x}{2}) d x

Multiply

nπ \frac{x}{2} : \frac{πn x}{2}

= \int cos (\frac{πn x}{2}) d x

Apply u-substitution

= \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

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