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

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

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

\int_{0}^{π} (sin^{2} (x)) d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{π} sin^{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}

x \to 0 lim (\frac{cos ( 10 x ) - 1}{x ^{2}})

\int (4 x + 1)^{2} e^{2 x} d x

\int cos (\frac{2}{3} x) d x

y^{^{''}} + 4 y^{^{'}} + 3 y = 20 t e^{5 t}

\frac{d y}{d x} = \frac{4 x ^{2}}{4 + x ^{3}}

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