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

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

\int_{0}^{2 π} 4 cos^{2} (x) d x

4 π

Decimal Notation

12.56637 \dots

Solution steps

\int_{0}^{2 π} 4 cos^{2} (x) d x

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} (x) d x

Rewrite using trig identities

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

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 x) d x

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 x + \int_{0}^{2 π} cos (2 x) d x)

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos (2 x) d x = 0

= 4 \cdot \frac{1}{2} (2 π + 0)

Simplify

4 \cdot \frac{1}{2} (2 π + 0) : 4 π

= 4 π

\int_{0}^{y} 1 d x

\int_{0}^{π} x sin (\frac{x}{2}) d x

\int_{0}^{1} a + b x^{2} d x

\int_{0}^{1} \frac{1 - cos ( x )}{x ^{2}} d x

\int_{0}^{\frac{π}{2}} \frac{1}{1 + sin ( x )} d x

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