Function not piecewise continuous

Question

I would like to find a function $f$ such that $$ \left|\int_a^b f(x)\ dx \right| > \int_a^b |f(x)|\ dx $$ where the integral should be understand in the Riemann sense.

Of course, $f$ shouldn't be piecewise continuous.

there is no such function, it can be proved that the opposite is always true. — tortue, Dec 01 '19 at 12:21

score 0 · Answer 1 · answered Dec 01 '19 at 12:14

0

Your inequality is always false. For example see here for a proof of the opposite inequality.

answered Dec 01 '19 at 12:14

Function not piecewise continuous

1 Answers1