What is the integral from 0 to 2pi of 9cos^2(x) ?

The integral from 0 to 2pi of 9cos^2(x) is 9pi

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 9cos^2(x)

\int_{0}^{2 π} 9 cos^{2} (x) d x

9 π

Decimal

28.27433 \dots

Solution steps

\int_{0}^{2 π} 9 cos^{2} (x) d x

Take the constant out:

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

= 9 \cdot \int_{0}^{2 π} cos^{2} (x) d x

Rewrite using trig identities

= 9 \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

= 9 \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

= 9 \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

= 9 \cdot \frac{1}{2} (2 π + 0)

Simplify

9 \cdot \frac{1}{2} (2 π + 0) : 9 π

= 9 π

\int_{0}^{2 a} e^{x} x^{2} d x

\int_{- 2}^{2} - 5 - x^{2} d x

\int_{0}^{2 π} 1 - cos^{2} (x) d x

\int_{0}^{1} 25 - x^{2} d x

\int_{1}^{9} \frac{9}{x} d x

What is the integral from 0 to 2pi of 9cos^2(x) ?
The integral from 0 to 2pi of 9cos^2(x) is 9pi