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

In summary, the conversation discusses the integration of cos(8x^2) in multivariable calculus. The individual attempted to solve it using various methods and resources, but was unable to find a solution. The conversation ends with the realization that the answer is 0.
  • #1
omonoid
18
0
Integral of cos(8x^2)? multivariable calc

Homework Statement



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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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  • #2


...dy dx?
 
  • #3


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:

1. What is the formula for finding the integral of cos(8x^2)?

The formula for finding the integral of cos(8x^2) is ∫cos(8x^2) dx = (1/8√2π)∫e^(-u^2/16) du, where u = 2x√2.

2. How do you solve the integral of cos(8x^2)?

To solve the integral of cos(8x^2), you can use the substitution method where u = 2x√2. Then, the integral becomes ∫cos(8x^2) dx = (1/8√2π)∫e^(-u^2/16) du. You can then use the formula for the integral of e^(-u^2) to solve for the final answer.

3. What is the significance of the constant 8 in the integral of cos(8x^2)?

The constant 8 in the integral of cos(8x^2) represents the frequency of the cosine function. It determines how many cycles of the cosine function will be included in the interval being integrated.

4. Is it possible to evaluate the integral of cos(8x^2) without using the substitution method?

Yes, it is possible to evaluate the integral of cos(8x^2) without using the substitution method. You can use other techniques such as integration by parts or trigonometric identities to simplify the integral before solving it.

5. Can the integral of cos(8x^2) be extended to multivariable calculus?

Yes, the integral of cos(8x^2) can be extended to multivariable calculus. In this case, the integral will become a double or triple integral, depending on the number of variables involved. The substitution method can still be used to solve the integral in multiple dimensions.

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