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

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

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integral from 0 to pi of sin^2(θ)

\int_{0}^{π} sin^{2} (θ) d θ

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{π} sin^{2} (θ) d θ

Rewrite using trig identities

= \int_{0}^{π} \frac{1 - cos ( 2 θ )}{2} d θ

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 θ) d θ

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 θ - \int_{0}^{π} cos (2 θ) d θ)

\int_{0}^{π} 1 d θ = π

\int_{0}^{π} cos (2 θ) d θ = 0

= \frac{1}{2} (π - 0)

Simplify

\frac{1}{2} (π - 0) : \frac{π}{2}

= \frac{π}{2}

n \to \infty lim (x + \frac{x}{n})

\int (x^{2} - 2 x + 5) e^{x} d x

\int cos (- 2 x) d x

\frac{d x}{d t} + x = 3 e^{t}

y^{^{'}} - y = e^{3 x}

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