What is the integral from 0 to pi/2 of 4sin(x/2) ?

The integral from 0 to pi/2 of 4sin(x/2) is 8(-1/(sqrt(2))+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/2 of 4sin(x/2)

\int_{0}^{\frac{π}{2}} 4 sin (\frac{x}{2}) d x

8 (- \frac{1}{2} + 1)

Decimal

2.34314 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 4 sin (\frac{x}{2}) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{2}} sin (\frac{x}{2}) d x

Apply u-substitution

= 4 \cdot \int_{0}^{\frac{π}{4}} sin (u) \cdot 2 d u

Take the constant out:

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

= 4 \cdot 2 \cdot \int_{0}^{\frac{π}{4}} sin (u) d u

Use the common integral:

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

= 4 \cdot 2 [- cos (u)]_{0}^{\frac{π}{4}}

Simplify

= 8 [- cos (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

- \frac{1}{2} + 1

= 8 (- \frac{1}{2} + 1)

What is the integral from 0 to pi/2 of 4sin(x/2) ?
The integral from 0 to pi/2 of 4sin(x/2) is 8(-1/(sqrt(2))+1)