What is the integral of sin(1/2 x) ?

The integral of sin(1/2 x) is -2cos(1/2 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(1/2 x)

\int sin (\frac{1}{2} x) d x

- 2 cos (\frac{1}{2} x) + C

Solution steps

\int sin (\frac{1}{2} x) d x

Apply u-substitution

: \int sin (u) \cdot 2 d u

= \int sin (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = \frac{1}{2} x

= 2 (- cos (\frac{1}{2} x))

Simplify

= - 2 cos (\frac{1}{2} x)

Add a constant to the solution

= - 2 cos (\frac{1}{2} x) + C

3 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 x^{2} + 7 x + 3

\int_{1}^{3} \frac{3 x ^{2} - 7}{x ^{3}} d x

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

y^{^{''}} + 2 y^{^{'}} + 5 y = 6 sin (2 t)

\frac{d ^{2}}{d x ^{2}} (cos (5 x))

What is the integral of sin(1/2 x) ?
The integral of sin(1/2 x) is -2cos(1/2 x)+C