Riemann Integrable.

Asked Nov 03 '18 at 04:56

Active Nov 03 '18 at 05:00

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We have some questions about Riemann integrable, so if $f,g$ are Riemann integrable
over $[a,b]$ denote by $f,g\in R[a,b]$, then $\max\{f,g\},\min\{f,g\}\in R[a,b]$.

So, it clearly ? , because in case $f<g$ then $\max\{f,g\}=g$

Since $g\in R[a,b]$ then $\max\{f,g\}\in R[a,b]$.

Similarly in case $g<f$.

Can some check that it true ?

edited Nov 03 '18 at 05:00

Chinnapparaj R

11,589

asked Nov 03 '18 at 04:56

panama wannawe

2

What if sometimes $f(x)>g(x)$ and then for another part of the interval we have $g(x)>f(x)$? – Clayton Nov 03 '18 at 04:59
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You can write $\max{f,g}$ ($\min$ too) as sum and product involving $f$ and $g$. – Lucas Nov 03 '18 at 05:05
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Here is a Riemann sum approach or use the trick suggested by@LucasCorrêa. – RRL Nov 03 '18 at 05:10
Thanks, everyone. – panama wannawe Nov 03 '18 at 05:11

Riemann Integrable.

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