Is this integration correct

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This will result in \int\stackrel{0}{-a}x(t)d(t) becoming \int\stackrel{a}{0}x(-t)d(t). Therefore, the integral becomes \int\stackrel{a}{0}x(-t)d(t) = \int\stackrel{a}{0}x(t)(-dt). In summary, to transform \int\stackrel{0}{-a}x(t)d(t) to \int\stackrel{a}{0}x(-t)d(t), use the substitution u = -t, du = - dt in both the integrand and the limits.
  • #1
machinarium
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I forgot all about integral so I need some help from you.
[tex]\int[/tex][tex]\stackrel{0}{-a}[/tex]x(t)dt=[tex]\int[/tex][tex]\stackrel{0}{a}[/tex]x(t)d(-t)=[tex]\int[/tex][tex]\stackrel{0}{a}[/tex]x(t)(-dt)

Please explain it to me. I want to transform [tex]\int[/tex][tex]\stackrel{0}{-a}[/tex]x(t)d(t) to [tex]\int[/tex][tex]\stackrel{a}{0}[/tex]x(-t)d(t) but don't know how.
 
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  • #2
machinarium said:
I forgot all about integral so I need some help from you.
[tex]\int[/tex][tex]\stackrel{0}{-a}[/tex]x(t)dt=[tex]\int[/tex][tex]\stackrel{0}{a}[/tex]x(t)d(-t)=[tex]\int[/tex][tex]\stackrel{0}{a}[/tex]x(t)(-dt)

Please explain it to me. I want to transform [tex]\int[/tex][tex]\stackrel{0}{-a}[/tex]x(t)d(t) to [tex]\int[/tex][tex]\stackrel{a}{0}[/tex]x(-t)d(t) but don't know how.

Use the substitution u = -t, du = - dt in both the integrand and the limits.
 

1. What is an integration in science?

An integration in science refers to the process of combining different pieces of information or data to form a comprehensive understanding or explanation of a particular phenomenon or concept.

2. How do you know if an integration is correct?

An integration is considered correct if it is supported by evidence and can be replicated by other scientists using the same methods and data.

3. What factors should be considered when evaluating the correctness of an integration?

Some factors to consider when evaluating the correctness of an integration include the reliability and validity of the data, the consistency of the results with existing knowledge and theories, and the potential for alternative explanations.

4. Can an integration be considered correct if it is not widely accepted by the scientific community?

No, an integration is not considered correct unless it is widely accepted and supported by the scientific community. This helps to ensure that the integration has been thoroughly evaluated and has withstood criticism and scrutiny from other experts in the field.

5. How can we prevent incorrect integrations in science?

To prevent incorrect integrations in science, it is important to use rigorous methods and carefully evaluate the evidence and data. Collaborating with other scientists and seeking peer review can also help to identify any potential errors or biases in the integration.

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