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

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

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

\int_{- 2 π}^{- π} cos^{2} (x) d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{- 2 π}^{- π} cos^{2} (x) d x

Rewrite using trig identities

= \int_{- 2 π}^{- 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

= \frac{1}{2} \cdot \int_{- 2 π}^{- 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

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

\int_{- 2 π}^{- π} 1 d x = π

\int_{- 2 π}^{- π} cos (2 x) d x = 0

= \frac{1}{2} (π + 0)

Simplify

\frac{1}{2} (π + 0) : \frac{π}{2}

= \frac{π}{2}

\frac{d}{d x} ((- sin (x))^{2})

x \to 0 lim (x^{2} + 5)

\int \frac{1}{2 - 5 x ^{2}} d x

\int_{3}^{9} t^{2} ln (4 t) d t

\frac{d}{d x} (\frac{( sin ( x ) )}{1 + cos ( x )})

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