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

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

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

\int_{0}^{2 π} π cos^{2} (x) d x

π^{2}

Decimal Notation

9.86960 \dots

Solution steps

\int_{0}^{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_{0}^{2 π} cos^{2} (x) d x

Rewrite using trig identities

= π \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

= π \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

= π \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

= π \frac{1}{2} (2 π + 0)

Simplify

π \frac{1}{2} (2 π + 0) : π^{2}

= π^{2}

\frac{d}{d x} (ab)

\int \frac{8 x + 10}{2 x ^{2} + 5 x} d x

\int \frac{1}{x 256 x ^{2} - 256} d x

x \to 1 - lim ((x - 1)^{2} f (x))

cot (x^{7})

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