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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2sin((npix)/2)

\int 2 sin (\frac{nπ x}{2}) d x

- \frac{4}{πn} cos (\frac{πn}{2} x) + C

Solution steps

\int 2 sin (\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 sin (\frac{nπ x}{2}) d x

\frac{nπ x}{2} = \frac{nπ}{2} x

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

Apply u-substitution

: \int \frac{2 sin ( u )}{πn} d u

= 2 \cdot \int \frac{2 sin ( 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 sin (u) d u

Use the common integral:

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

= 2 \cdot \frac{2}{πn} (- cos (u))

Substitute back

u = \frac{nπ}{2} x

= 2 \cdot \frac{2}{πn} (- cos (\frac{nπ}{2} x))

Simplify

2 \cdot \frac{2}{πn} (- cos (\frac{nπ}{2} x)) : - \frac{4}{πn} cos (\frac{πn}{2} x)

= - \frac{4}{πn} cos (\frac{πn}{2} x)

Add a constant to the solution

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

\int \frac{1}{x ^{2} ( x ^{2} + 25 )} d x

\int (\frac{x}{2} + \frac{3}{2})^{2} d x

\int 72 d x

\int x^{3} (9 + x^{4})^{5} d x

\int \frac{e ^{- 2 x}}{4} d x

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