What is the integral from 0 to 2 of 2cos((npix)/2) ?

The integral from 0 to 2 of 2cos((npix)/2) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of 2cos((npix)/2)

\int_{0}^{2} 2 cos (\frac{nπ x}{2}) d x

0

Solution steps

\int_{0}^{2} 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_{0}^{2} cos (\frac{nπ x}{2}) d x

Apply u-substitution

: \int_{0}^{πn} \frac{2 cos ( u )}{πn} d u

= 2 \cdot \int_{0}^{πn} \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_{0}^{πn} cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{2}{πn} [sin (u)]_{0}^{πn}

Simplify

2 \cdot \frac{2}{πn} [sin (u)]_{0}^{πn} : \frac{4}{πn} [sin (u)]_{0}^{πn}

= \frac{4}{πn} [sin (u)]_{0}^{πn}

Compute the boundaries:

0

= \frac{4}{πn} \cdot 0

Simplify

= 0

\int_{1}^{4} 8 x d x

\int_{0}^{2} 3 x (x - 7) d x

\int_{- 6}^{0} 4 - 2 x d x

\int_{0}^{1} 2 π x e^{x} d x

\int_{0}^{2} \frac{1}{4 - x} d x

What is the integral from 0 to 2 of 2cos((npix)/2) ?
The integral from 0 to 2 of 2cos((npix)/2) is 0