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

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

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

\int_{- π}^{π} cos^{2} (x) d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{- π}^{π} cos^{2} (x) d x

Rewrite using trig identities

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

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (2 x) d x = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\frac{d}{d x} (\frac{4}{x ^{2} - 1})

y = x^{2} + 2 x + 6

x^{2}, x + 2, 0

x \to 0 lim (\frac{e ^{x} - 1}{3 x})

f (x) = (4 x - 7)^{\frac{1}{2}}, at x = 4

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