Solve Integral of cos(y^2) - Calculus

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    Calculus Integral
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Homework Help Overview

The discussion revolves around the integral of cos(y^2), a topic within calculus. Participants are exploring the nature of this integral and its potential representations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express cos(y^2) in different forms and questioning the possibility of reducing it to terms involving sin(y) and cos(y). There is also mention of functions related to gradients and the exploration of trigonometric identities.

Discussion Status

The discussion is active, with various interpretations being explored. Some participants suggest looking into the Cosine Fresnel Integral as a potential avenue for understanding the integral, while others express skepticism about simplifying cos(y^2) further.

Contextual Notes

There is a mention of the integral having no elementary solution, which may influence the direction of the discussion. Participants are navigating the constraints of the problem and the nature of the functions involved.

caaron3
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Can anyone help me with the integral of cos(y^2)?
 
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Possibly. Can you reduce cos(y^2) down and express it in terms of sin(y) and cos(y)?
 
not really. I'm finding functions, given the gradient...

((e^x)*cos(y^2))i - (2y(e^x)sin(y^2))j
 
I reckon you can. How about if you write cos(2y)=cos(y+y)=...
 
cristo - its cos (y^2), not 2y :(

caaron3 - it has no elementary solution, though if you really want some sort of a solution, the anti derivative is in terms of the Cosine Fresnel Integral, so look that up.
 

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