Which Quantity is Considered the Upper and Lower Limits in a Definite Integral?

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SUMMARY

The discussion clarifies the determination of upper and lower limits in definite integrals, specifically when integrating from a constant 'a' to a variable 'x'. The integral is expressed as ∫ax f(x) dx, where 'a' is the lower limit and 'x' is the upper limit. The confusion arises when the integral is presented in different formats, such as -∫xa f(x) dx, which can lead to misinterpretation. Understanding the notation and context is essential for accurate integration.

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wahaj
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When taking a definite integral that is bound by two points a and x where a is a constant and x is a variable, which quantity do I consider the upper limit of the integral and which quantity is the lower limit?
[tex]\int^a_x x[/tex]
this integral is written as
[tex]-\int^x_a x[/tex] in my book.
When I use integrals in my dynamics class I can easily tell which limit goes where but this is much tougher in math class because all I am given are random functions to integrate.
 
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You have to be told to integrate "from a to b".
 
ok. I always assumed it didn't really matter, I can't believe I got so many questions right doing what I did.
 

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