Integration (Lower - Upper) or (Upper - Lower)

[Ted_Grendy]

Hi all

I wanted to ask what the convention was when calculating a definite integral between 2 values, which of the two would we do:-

- Lower bound - Upper Bound
- Upper bound - Lower Bound

Where the lower bound value is the value at the bottom of the integral and the upper bound value is the value on the top of the integral?

What is the convention?

Thank you

 

[MarkFL]

According to the FTOC, we use:

[MATH]\int_a^b f(x)\,dx=F(b)-F(a)[/MATH] where [MATH]\frac{d}{dx}F(x)=f(x)[/MATH].

 

[Dr.Peterson]

I wanted to ask what the convention was when calculating a definite integral between 2 values, which of the two would we do:-

- Lower bound - Upper Bound
- Upper bound - Lower Bound

Where the lower bound value is the value at the bottom of the integral and the upper bound value is the value on the top of the integral?

What is the convention?

Note that it is not just a convention (which would be a more or less arbitrary choice that people have agreed to). It is a theorem -- your two choices give two different answers, and only one of them can be correct.

It's F(upper) minus F(lower).