What is the integral of cos(4θ)cos(-3θ) ?

The integral of cos(4θ)cos(-3θ) is 1/2 (sin(θ)+1/7 sin(7θ))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(4θ)cos(-3θ)

\int cos (4 θ) cos (- 3 θ) d θ

\frac{1}{2} (sin (θ) + \frac{1}{7} sin (7 θ)) + C

Solution steps

\int cos (4 θ) cos (- 3 θ) d θ

Simplify

cos (4 θ) cos (- 3 θ) : cos (3 θ) cos (4 θ)

= \int cos (3 θ) cos (4 θ) d θ

Rewrite using trig identities

= \int \frac{1}{2} (cos (7 θ) + cos (- θ)) d θ

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (7 θ) + cos (- θ) d θ

Simplify

cos (7 θ) + cos (- θ) : cos (θ) + cos (7 θ)

= \frac{1}{2} \cdot \int cos (θ) + cos (7 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

= \frac{1}{2} (\int cos (θ) d θ + \int cos (7 θ) d θ)

\int cos (θ) d θ = sin (θ)

\int cos (7 θ) d θ = \frac{1}{7} sin (7 θ)

= \frac{1}{2} (sin (θ) + \frac{1}{7} sin (7 θ))

Add a constant to the solution

= \frac{1}{2} (sin (θ) + \frac{1}{7} sin (7 θ)) + C

\int \frac{1}{t ^{2} 4 - t ^{2}} d t

\frac{\partial}{\partial x} (- 13 e^{x} sin (y) - 14 y)

\frac{d}{d a} (sin (a) - sin (6 a) + sin (5 a))

x \to 0 lim (e^{- 4 x})

y^{^{'}} = \frac{1.5 - 0.8 y}{0.5 + 0.8 x}

What is the integral of cos(4θ)cos(-3θ) ?
The integral of cos(4θ)cos(-3θ) is 1/2 (sin(θ)+1/7 sin(7θ))+C