Integral of cos(8x^2)? multivariable calc

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SUMMARY

The integral of cos(8x^2) was the main focus of the discussion, where the user initially struggled with the integration process. After reversing the order of integration and reviewing trigonometric identities, the user utilized a graphing calculator and Wolfram Alpha but received an unexpected result. Ultimately, the user discovered that the integral evaluates to 0 after extensive work and confusion.

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  • Understanding of multivariable calculus concepts
  • Familiarity with trigonometric identities
  • Experience using graphing calculators
  • Knowledge of integration techniques
NEXT STEPS
  • Research techniques for integrating oscillatory functions
  • Learn about the properties of definite integrals and their applications
  • Explore advanced integration methods, such as substitution and integration by parts
  • Study the use of computational tools like Wolfram Alpha for solving integrals
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Students and educators in multivariable calculus, mathematicians dealing with oscillatory integrals, and anyone seeking to improve their integration skills.

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Integral of cos(8x^2)? multivariable calc

Homework Statement



dA1w3.png


Homework Equations



none

The Attempt at a Solution



So i reversed the order...

jZ4n0.png


and couldn't figure out how to integrate cos(8x^2). I looked at my trig identities, tried on my graphing calc, and even wolfram alpha gave me a strange answer that i can't use.

Either I'm doing something wrong, or missing something obvious.

Thanks
Jake
 
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...dy dx?
 


oh yeah. in my work i should have wrote dydx instead of dxdy good catch. wow. maybe i can solve it now.

lets see...wow... the answer was 0, after a page of work and a few hours of confusion
 
Last edited:

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