What is the integral of 2cos((npix)/2) ?

The integral of 2cos((npix)/2) is 4/(pin)sin((pinx)/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2cos((npix)/2)

\int 2 cos (\frac{nπ x}{2}) d x

\frac{4}{πn} sin (\frac{πn x}{2}) + C

Solution steps

\int 2 cos (\frac{nπ x}{2}) d x

Take the constant out:

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

= 2 \cdot \int cos (\frac{nπ x}{2}) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{πn} d u

= 2 \cdot \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

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

Use the common integral:

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

= 2 \cdot \frac{2}{πn} sin (u)

Substitute back

u = \frac{n x π}{2}

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

Simplify

2 \cdot \frac{2}{πn} sin (\frac{n x π}{2}) : \frac{4}{πn} sin (\frac{πn x}{2})

= \frac{4}{πn} sin (\frac{πn x}{2})

Add a constant to the solution

= \frac{4}{πn} sin (\frac{πn x}{2}) + C

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

\frac{d y}{d x} = 3^{e^{2 x}} y^{2}

\frac{9}{8 x ^{4}}

x \to 1 lim (\frac{8}{1 - x})

2 x^{^{''}} + 4 x^{^{'}} + 8 x = 0

What is the integral of 2cos((npix)/2) ?
The integral of 2cos((npix)/2) is 4/(pin)sin((pinx)/2)+C