Small Integration: Learn How to Navigate the Second Line

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SUMMARY

The discussion focuses on integrating functions across a symmetric interval using the technique of splitting the integral. Specifically, it outlines the method for calculating the integral of a function f(t) from -L to L by breaking it into two parts: the integral from 0 to L and the integral from -L to 0, where the latter is transformed by substituting -t. This approach allows for the removal of absolute value signs and facilitates standard integration techniques. Finally, the limits are substituted, and L is allowed to approach infinity to complete the process.

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  • Knowledge of limits and their application in calculus
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electronic engineer
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Hello.I actually didn't know exactly how do we get to the second line with this integration.
 

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Integrate this by splitting up the interval on which it is done:

[tex]\int^L_{-L} f(t) dt = \int^L_{0} f(t) dt + \int^0_{-L} f(-t) dt[/tex]

Then you'll be able to remove the '| |' and integrate it normally. When you're done with the integration, just substitute in the limits and let L approach infinity.
 

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