What is the integral from 0 to 2pi of 4cos^2(θ) ?

The integral from 0 to 2pi of 4cos^2(θ) is 4pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2pi of 4cos^2(θ)

\int_{0}^{2 π} 4 cos^{2} (θ) d θ

4 π

Decimal Notation

12.56637 \dots

Solution steps

\int_{0}^{2 π} 4 cos^{2} (θ) d θ

Take the constant out:

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

= 4 \cdot \int_{0}^{2 π} cos^{2} (θ) d θ

Rewrite using trig identities

= 4 \cdot \int_{0}^{2 π} \frac{1 + cos ( 2 θ )}{2} d θ

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{2 π} 1 + cos (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

= 4 \cdot \frac{1}{2} (\int_{0}^{2 π} 1 d θ + \int_{0}^{2 π} cos (2 θ) d θ)

\int_{0}^{2 π} 1 d θ = 2 π

\int_{0}^{2 π} cos (2 θ) d θ = 0

= 4 \cdot \frac{1}{2} (2 π + 0)

Simplify

4 \cdot \frac{1}{2} (2 π + 0) : 4 π

= 4 π

\int_{1}^{2} \frac{5 - 7 x}{x ^{3}} d x

\int_{0}^{l n (4)} tanh (x) d x

\int_{0}^{1} x^{2} - 4 x + 7 d x

\int_{0}^{\frac{π}{6}} 3 cos (x) + 1 d x

\int_{0}^{2} x 3^{- x^{2}} d x

What is the integral from 0 to 2pi of 4cos^2(θ) ?
The integral from 0 to 2pi of 4cos^2(θ) is 4pi