Integrating sin(x^2) using substitution method

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In summary, the general formula for integrating sin(x^2) is not known and it requires numerical methods for approximation. Substitution can be used to integrate sin(x^2) and there is no specific method for integration. To check if the integration is correct, you can differentiate the answer and see if it results in the original function. A calculator or computer program can also be used for numerical integration, but it will only provide an approximation.
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hytuoc
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how to integrate sin(x^2)?
 
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It can be put in connection with S,which is one of the Fresnel integrals.

It's noit expressible through "elementary" functions.

Daniel.
 
  • #3

To integrate sin(x^2), we can use the substitution method. Let u = x^2, then du = 2x dx. We can rewrite the integral as ∫sin(u) * (1/2x) du. Using the formula for the integral of sin(u), we get ∫sin(u) * (1/2x) du = -(1/2x) * cos(u) + C = -(1/2x) * cos(x^2) + C. Therefore, the integral of sin(x^2) is -(1/2x) * cos(x^2) + C.
 

1. What is the general formula for integrating sin(x^2)?

The general formula for integrating sin(x^2) is not known, as it does not have an elementary antiderivative. However, it can be approximated using numerical methods.

2. Can I use substitution to integrate sin(x^2)?

Yes, substitution can be used to integrate sin(x^2). One possible substitution is u = x^2, which can simplify the integral to a form that can be integrated using other techniques.

3. Is there a specific method for integrating sin(x^2)?

There is no specific method for integrating sin(x^2), as it does not have an elementary antiderivative. Different techniques such as substitution, integration by parts, or numerical methods can be used to approximate the integral.

4. How do I know if I have integrated sin(x^2) correctly?

One way to check if you have integrated sin(x^2) correctly is to differentiate your answer and see if it results in the original function sin(x^2). If it does, then you have integrated it correctly.

5. Can I use a calculator to integrate sin(x^2)?

Yes, you can use a calculator or a computer program to numerically integrate sin(x^2). However, it is important to note that the result will be an approximation and not an exact solution.

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