1. The problem statement, all variables and given/known data What I want to show is this: ∫|x+y| ≤ ∫|x| + ∫|y| 2. Relevant equations |x+y| ≤ |x| + |y| 3. The attempt at a solution So I thought if I used the triangle inequality I could get to something along the lines of: Lets g belong to the real numbers ∫|x+y| = ∫|x+g-g+y|≤ ∫|x+g| + |y-g|= ∫|x+g| + ∫|y-g| As g belongs to the reals it can be zero meaning ∫|x+y| ≤ ∫|x| + ∫|y|. Now the problem with this is that is uses the triangle inequality and I have no idea if the triangle inequality works this way, and if it does I need to prove it, and I have no idea about where to start that from.