What is the integral of cos^4(θ) ?

The integral of cos^4(θ) is cos^3(θ)sin(θ)+3/8 (θ-1/4 sin(4θ))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^4(θ)

\int cos^{4} (θ) d θ

cos^{3} (θ) sin (θ) + \frac{3}{8} (θ - \frac{1}{4} sin (4 θ)) + C

Solution steps

\int cos^{4} (θ) d θ

Simplify

cos^{4} (θ) : cos^{3} (θ) cos (θ)

= \int cos^{3} (θ) cos (θ) d θ

Apply Integration By Parts

: cos^{3} (θ) sin (θ) - \int - 3 cos^{2} (θ) sin^{2} (θ) d θ

= cos^{3} (θ) sin (θ) - \int - 3 cos^{2} (θ) sin^{2} (θ) d θ

\int - 3 cos^{2} (θ) sin^{2} (θ) d θ = - \frac{3}{8} (θ - \frac{1}{4} sin (4 θ))

= cos^{3} (θ) sin (θ) - (- \frac{3}{8} (θ - \frac{1}{4} sin (4 θ)))

Simplify

= cos^{3} (θ) sin (θ) + \frac{3}{8} (θ - \frac{1}{4} sin (4 θ))

Add a constant to the solution

= cos^{3} (θ) sin (θ) + \frac{3}{8} (θ - \frac{1}{4} sin (4 θ)) + C

\frac{d}{d x} (6 x^{3})

2 x y \frac{d y}{d x} = x^{2} + 2 y^{2}

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

f (x) = cot^{3} (x)

y = 2 x, y = 3 x - 4, y = 0

What is the integral of cos^4(θ) ?
The integral of cos^4(θ) is cos^3(θ)sin(θ)+3/8 (θ-1/4 sin(4θ))+C