What is the integral of cos(θ/2) ?

The integral of cos(θ/2) is 2sin(θ/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(θ/2)

\int cos (\frac{θ}{2}) d θ

2 sin (\frac{θ}{2}) + C

Solution steps

\int cos (\frac{θ}{2}) d θ

Apply u-substitution

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

= \int cos (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 cos (u) d u

Use the common integral:

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

= 2 sin (u)

Substitute back

u = \frac{θ}{2}

= 2 sin (\frac{θ}{2})

Add a constant to the solution

= 2 sin (\frac{θ}{2}) + C

\frac{d}{d x} (x^{2} sin (x) + 2 x cos (x) - 2 sin (x))

\int_{9}^{16} \frac{1}{9 - x} d x

\frac{d}{d x} (- \frac{11}{( x - 3 ) ^{2}})

\frac{\partial}{\partial x} (x y e^{- x - y})

x \to - 3 - lim (\frac{x ^{2}}{x + 3})