What is the integral from-pi to 2pi of picos^2(x) ?

The integral from-pi to 2pi of picos^2(x) is (3pi^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-pi to 2pi of picos^2(x)

\int_{- π}^{2 π} π cos^{2} (x) d x

\frac{3 π ^{2}}{2}

Decimal Notation

14.80440 \dots

Solution steps

\int_{- π}^{2 π} π cos^{2} (x) d x

Take the constant out:

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

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

Rewrite using trig identities

= π \cdot \int_{- π}^{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

= π \frac{1}{2} \cdot \int_{- π}^{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

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

\int_{- π}^{2 π} 1 d x = 3 π

\int_{- π}^{2 π} cos (2 x) d x = 0

= π \frac{1}{2} (3 π + 0)

Simplify

π \frac{1}{2} (3 π + 0) : \frac{3 π ^{2}}{2}

= \frac{3 π ^{2}}{2}

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 2)

\int \frac{49 + x ^{2}}{x} d x

x \to 2 + lim (\frac{5 + x}{2 - x})

\frac{1}{s ^{6}}

e^{- s t}

What is the integral from-pi to 2pi of picos^2(x) ?
The integral from-pi to 2pi of picos^2(x) is (3pi^2)/2