Real Integral Additivity
Why
Is the sum of two functions integrable? What is their sum.
Result
Suppose $f, g: \R \to \R $ are integrable.
Then the function $f+g$ is integrable and
\[ \int f + g = \int f + \int g \]
Is the sum of two functions integrable? What is their sum.
\[ \int f + g = \int f + \int g \]