How to perform this integration?

In summary, integration methods are chosen based on the type of function and desired accuracy, with commonly used ones being the trapezoidal rule, Simpson's rule, and Gaussian quadrature. The purpose of integration is to find the area under a curve or definite integral of a function and is used in various fields. The limits of integration are determined by the problem at hand and can be found in the problem statement or context. Common sources of error in integration include rounding, truncation, and integration errors, which can be minimized by using more accurate methods or increasing intervals. Accuracy can be checked through error bound formulas and comparison with known solutions.
  • #1
xmtung
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Homework Statement



The integration:
 

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  • #2
...I can't view the picture...try re-upping it as a jpeg or something so
 
  • #3
I re-upload the pic. The integration is that ∫cos(kx)exp[(-αt)K^2] dkfrom zero to infinity
 

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  • #4
Convert cos(kx) to (exp(ikx)+exp(-ikx))/2. Combine the exponentials and complete the squares in the exponents. Now do a change of variable and use the known result for exp(-Cx^2).
 

1. How do I choose the appropriate integration method?

The choice of integration method depends on the type of function being integrated and the desired accuracy. Some commonly used methods include the trapezoidal rule, Simpson's rule, and Gaussian quadrature.

2. What is the purpose of integration?

Integration is the process of finding the area under a curve or the definite integral of a function. It is used in various fields of science and engineering to solve problems involving continuous quantities such as velocity, acceleration, and force.

3. How do I set up the limits of integration?

The limits of integration are determined by the problem at hand. They represent the range over which the integral is being evaluated. In most cases, the limits are given in the problem statement or can be determined from the context.

4. What are some common sources of error in integration?

Some common sources of error in integration include rounding errors, truncation errors, and integration errors due to numerical approximations. These errors can be minimized by using more accurate methods or increasing the number of intervals used.

5. Is there a way to check the accuracy of my integration?

Yes, there are methods to check the accuracy of integration such as the error bound formula and comparison with known exact solutions. It is always a good practice to check the accuracy of your integration results to ensure the validity of your calculations.

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