What is the integral of asin(θ)(1+sin(θ)) ?

The integral of asin(θ)(1+sin(θ)) is a(-cos(θ)+1/2 (θ-1/2 sin(2θ)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of asin(θ)(1+sin(θ))

\int a sin (θ) (1 + sin (θ)) d θ

a (- cos (θ) + \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))) + C

Solution steps

\int a sin (θ) (1 + sin (θ)) d θ

Take the constant out:

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

= a \cdot \int sin (θ) (1 + sin (θ)) d θ

Expand

sin (θ) (1 + sin (θ)) : sin (θ) + sin^{2} (θ)

= a \cdot \int sin (θ) + sin^{2} (θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= a (\int sin (θ) d θ + \int sin^{2} (θ) d θ)

\int sin (θ) d θ = - cos (θ)

\int sin^{2} (θ) d θ = \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))

= a (- cos (θ) + \frac{1}{2} (θ - \frac{1}{2} sin (2 θ)))

Add a constant to the solution

= a (- cos (θ) + \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))) + C

\frac{3}{x}, 12 x, \frac{x}{3}

\int (t^{2} - 2 cos (t)) d t

f (x) = 2 x^{2} - 3 x + 1

x \to 0 lim (\frac{100}{x ^{2}})

\int (x - 6) sin (π x) d x

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