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

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

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

\int_{0}^{π} cos^{2} (x) d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{π} cos^{2} (x) d x

Rewrite using trig identities

= \int_{0}^{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}^{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}^{π} 1 d x + \int_{0}^{π} cos (2 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{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 x}{d t} = x - 2 x^{2}

\frac{1}{5}

x^{2}, x, [\frac{1}{4}, 1]

\frac{d}{d x} (x^{2} arctan (3 x))

y = 1 + 2 x, y = \frac{( 3 + x )}{3}

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