Changing the limits of integration

In summary, "changing the limits of integration" is the process of altering the range of an integral. This can make it easier to evaluate the integral or to solve for a different variable. It can be done using substitutions, change of variables, or integration by parts. Some common mistakes include forgetting to adjust the limits and not considering restrictions on the new variable. This technique is commonly used in mathematics, physics, engineering, and other fields where integrals are used.
  • #1
jinksys
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! SOLVED !

This isn't a homework problem, just an equation in my chapter. I don't see how the two integrals pointed to by the blue arrows become the integral pointed to by the red arrow. I know that if you swap the limits of integration, you change the sign of the integral. However, how do you change the -pi to pi in the second integral?

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  • #2
Use the substitution u=-x
 
  • #3
Of course, thanks.
 

What is "changing the limits of integration"?

"Changing the limits of integration" refers to the process of altering the values that define the range of an integral. This can be done to simplify the calculation of the integral or to solve for a different variable.

Why would someone want to change the limits of integration?

Changing the limits of integration can make it easier to evaluate an integral, especially when the original limits are complex. It can also help to solve for a different variable, making it a useful technique in many areas of mathematics and science.

How do you change the limits of integration?

To change the limits of integration, you can use a substitution or a change of variables. This involves replacing the original variable with a new one and adjusting the limits accordingly. Another method is to use integration by parts, which allows you to manipulate the limits of integration in certain cases.

What are some common mistakes when changing the limits of integration?

One common mistake is forgetting to adjust the limits when using a substitution or change of variables. It is also important to check for any discontinuities or singularities in the new limits, as these can affect the accuracy of the integral. Additionally, it is important to be aware of any restrictions on the new variable that may affect the integration.

In what fields is changing the limits of integration commonly used?

Changing the limits of integration is commonly used in mathematics, physics, engineering, and other fields where integrals are used. It is particularly useful in solving problems involving area, volume, and work, as well as in solving differential equations and other mathematical models.

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