What is the integral from 0 to pi/3 of 3sin(x/2) ?

The integral from 0 to pi/3 of 3sin(x/2) is 6(-(sqrt(3))/2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi/3 of 3sin(x/2)

\int_{0}^{\frac{π}{3}} 3 sin (\frac{x}{2}) d x

6 (- \frac{3}{2} + 1)

Decimal

0.80384 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 3 sin (\frac{x}{2}) d x

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{3}} sin (\frac{x}{2}) d x

Apply u-substitution

: \int_{0}^{\frac{π}{6}} sin (u) \cdot 2 d u

= 3 \cdot \int_{0}^{\frac{π}{6}} sin (u) \cdot 2 d u

Take the constant out:

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

= 3 \cdot 2 \cdot \int_{0}^{\frac{π}{6}} sin (u) d u

Use the common integral:

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

= 3 \cdot 2 [- cos (u)]_{0}^{\frac{π}{6}}

Simplify

= 6 [- cos (u)]_{0}^{\frac{π}{6}}

Compute the boundaries:

- \frac{3}{2} + 1

= 6 (- \frac{3}{2} + 1)

\int_{1}^{2} (5 x^{4} - 3) ln (x) d x

\int_{1}^{3} 4^{5 x} d x

\int_{2}^{5} (- 3 x + 4) d x

\int_{0}^{2 π} t d t

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 4) d x

What is the integral from 0 to pi/3 of 3sin(x/2) ?
The integral from 0 to pi/3 of 3sin(x/2) is 6(-(sqrt(3))/2+1)