Improper integral and rectangle method

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SUMMARY

The discussion focuses on the application of the rectangle method for approximating definite integrals, specifically addressing improper integrals where the upper limit approaches infinity. The rectangle method is defined as \int_{a}^{b}f(x)dx \sim \sum_{n=0}^{N}f(a+nh)h, with the condition that as b approaches infinity, the upper limit N must also approach infinity. This leads to the need for careful consideration in defining the method for improper integrals.

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  • Understanding of definite integrals
  • Familiarity with the rectangle method for numerical integration
  • Knowledge of improper integrals and their properties
  • Basic calculus concepts, including limits
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  • Research the properties of improper integrals in calculus
  • Learn about numerical integration techniques beyond the rectangle method
  • Explore convergence criteria for improper integrals
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Students and professionals in mathematics, particularly those studying calculus, numerical methods, or anyone interested in understanding the nuances of improper integrals and numerical approximation techniques.

lokofer
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Improper integral and "rectangle" method

If we have a definite integral then..using "rectangle" method we can get the approximation:

[tex]\int_{a}^{b}f(x)dx \sim \sum_{n=0}^{N}f(a+nh)h[/tex]

My question is..how do you define this method when b-->oo (Imporper integral?)...:confused: :confused:
 
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The upper limit N must be such that a + Nh = b. If b -> oo, then make the upper limit N = oo.
 

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