Area under Arc of Sine Function

Theorem

$\ds \int_0^\pi \sin x \rd x = 2$

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Proof

$\ds \int_0^\pi \sin x \rd x$

$=$

$\ds \bigintlimits {-\cos x} 0 \pi$

Primitive of Sine Function

$\ds $

$=$

$\ds 2$

Cosine of $\pi$, Cosine of $0 \degrees$

$\blacksquare$