Fresnel sine integral

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For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of $90\,^\circ$ is measured as $\pi/2$.

Definition

The Fresnel sine integral, which we here denote by $S$, is defined as:

$S(x) := \int_0^x \sin(t^2) \, dt$