Fresnel cosine integral

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This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
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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 cosine integral, which we denote here by C, is defined as a definite integral of the cos(x^2) function:

C(x) = \int_0^x \cos(t^2) \, dt