Double integration with cos x^2

In summary, the conversation is about integrating the function ycos(x^2) with parameters dx=y^2 to 1 and dx=0 to 1. The main problems are identifying the double angle identity for cos(x^2) and integrating it with respect to x^2. The conversation also discusses the possibility of reparametrizing the region of integration to find a solution.
  • #1
raynoodles
4
0
ok so I have the problem ycos(x^2)dxdy with parameters dx=y^2 to 1 and dx=0 to 1
the first problem I have is integrating cos with respect to x^2. is it a double angle identity? the second is how do I go further if Y^2 gets added into the mix later?
The attempts I have made have made me even more confused than before. I looked up how I could integrate cos x^2 and could not find a clear answer.
Help is appreciated.
 
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  • #2
Did you copy the limits of integration correctly?
Should it be x going from y^2 to 1 and then y going from 0 to 1?
 
  • #3
raynoodles said:
I could integrate cos x^2 and could not find a clear answer.
Help is appreciated.

What is the identity of cosx^2? if you don't know then look it up in your book.
 
  • #4
It can't be expressed in terms of elementary functions, look up the Cosine Fresnel integral for the solution.
 
  • #5
Not so fast.
Try reparametrizing your region of integration. If you first integrate wrt y, then wrt x you may find a solution. (Hint: You will).
 
  • #6
O sorry I should have read the whole question, Mainly just read post 3 and replied to that.
 

Related to Double integration with cos x^2

1. What is double integration with cos x^2?

Double integration with cos x^2 refers to the process of finding the area under a curve that is defined by the function cos x^2, using integration. This involves performing integration twice, once for each variable in the equation.

2. Why is double integration with cos x^2 important?

Double integration with cos x^2 is important in many areas of science, including physics, engineering, and mathematics. It allows us to calculate the area under a curve, which has many applications in real-world problems, such as determining the work done by a force or the displacement of an object.

3. How do you perform double integration with cos x^2?

To perform double integration with cos x^2, you first need to determine the limits of integration for both variables in the equation. Then, you can use integration rules and techniques to solve the integral and find the area under the curve. This process may involve using substitution, integration by parts, or other integration methods.

4. What are the challenges of double integration with cos x^2?

One of the main challenges of double integration with cos x^2 is determining the limits of integration for both variables, as this can be a complex process. Additionally, the integration itself can be difficult and may require advanced techniques or software to solve. It is also important to be aware of any special cases or conditions that may affect the integration process.

5. How is double integration with cos x^2 used in real-world applications?

Double integration with cos x^2 has many real-world applications, such as calculating the work done by a force in physics, determining the volume of a solid in engineering, and finding the area under a curve in mathematics. It is also used in fields such as economics, statistics, and computer science to model and solve various problems.

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