hello could someone help me with this problem i have an ans but i dont think its worked fully.thanks
Prove that if f and g are integrable functions on [a,b] then f+g is integrable and
Let be a partition of with .
recall that and over the interval.
now, for any partition ,
---- (1)
---- (2)
So, let . since and are integrable on ,
such that
--- (3)
--- (4)
so, take which is a refinement of ..
by (2)
(from theorem or lemma)
by (3) and (4)
(from theorem or lemma)
by (1)
and so, which means is integrable on ..
for the second part, you can do it by showing one is greater or equal than the other and vice versa..