How Do You Integrate cos[(pi/9)(x^2)]?

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SUMMARY

The discussion focuses on the integration of the function cos[(π/9)(x²)], specifically addressing the indefinite integral ∫ cos(πx²/9) dx. Participants explore the substitution method, using U = (π/9)x², and derive the differential dU = (2π/9)x dx. The conversation also raises questions about the presence of integration limits and the need for trigonometric identities related to cos(x²), emphasizing the complexity of integrating such functions.

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  • Study the method of integration by substitution in calculus
  • Learn about Fresnel integrals for handling integrals of the form ∫ cos(x²) dx
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Homework Statement


Integrate cos[(pi/9)(x^2)


Homework Equations


Is there a trig identity for the cos(x^2) ?


The Attempt at a Solution



U=(pi/9)T^2
dU= [2(pi)/9] (T)dT dT= dU/ {[2(pi)/9 (T)]}

Substitute in get cosU dU/ {[2(pi)/9 (T)]} Now what?
 
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jmrec100 said:

Homework Statement


Integrate cos[(pi/9)(x^2)

Do you mean:

[tex]\int \cos\left(\frac{\pi x^2}{9}\right)dx[/itex] <br /> <br /> or something else? Are you given integration limits, or are you only asked for the indefinite integral?[/tex]
 

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