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

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

Popular >

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

\int_{0}^{2 π} (cos (x))^{2} d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{0}^{2 π} (cos (x))^{2} d x

Simplify

= \int_{0}^{2 π} cos^{2} (x) d x

Rewrite using trig identities

= \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

= \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

= \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

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\frac{2 x ^{2} + 6 x + 2}{x}

\int sec^{2} (x) tan (x) d x

(\frac{1}{x} + 2 y^{2} x) d x + (2 y x^{2} - cos (y)) d y = 0, y (1) = π

n = 1 \sum \infty (sin (3))^{n}

\frac{d}{d x} (e^{x + y} - 1)

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