What is the integral from-pi/2 to pi/2 of cos(nx) ?

The integral from-pi/2 to pi/2 of cos(nx) is (2sin((pin)/2))/(n)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-pi/2 to pi/2 of cos(nx)

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (n x) d x

\frac{2 sin ( \frac{πn}{2} )}{n}

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (n x) d x

Apply u-substitution

= \int_{- \frac{πn}{2}}^{\frac{πn}{2}} \frac{cos ( u )}{n} d u

Take the constant out:

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

= \frac{1}{n} \cdot \int_{- \frac{πn}{2}}^{\frac{πn}{2}} cos (u) d u

Use the common integral:

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

= \frac{1}{n} [sin (u)]_{- \frac{πn}{2}}^{\frac{πn}{2}}

Compute the boundaries:

2 sin (\frac{πn}{2})

= \frac{1}{n} \cdot 2 sin (\frac{πn}{2})

Simplify

= \frac{2 sin ( \frac{πn}{2} )}{n}

What is the integral from-pi/2 to pi/2 of cos(nx) ?
The integral from-pi/2 to pi/2 of cos(nx) is (2sin((pin)/2))/(n)