What is the integral from-1 to 1 of cos((pix)/2) ?

The integral from-1 to 1 of cos((pix)/2) is 4/pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 1 of cos((pix)/2)

\int_{- 1}^{1} cos (\frac{π x}{2}) d x

\frac{4}{π}

Decimal

1.27323 \dots

Solution steps

\int_{- 1}^{1} cos (\frac{π x}{2}) d x

Apply u-substitution

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

Take the constant out:

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

= \frac{2}{π} \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (u) d u

Use the common integral:

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

= \frac{2}{π} [sin (u)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= \frac{2}{π} \cdot 2

Simplify

= \frac{4}{π}

What is the integral from-1 to 1 of cos((pix)/2) ?
The integral from-1 to 1 of cos((pix)/2) is 4/pi