- #1

michonamona

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## Homework Statement

Suppose that f(x)=c for all x in [a,b]. Show that f is integrable and that [tex]\int ^{a}_{b}[/tex]f(x)dx = c(b-a)

## Homework Equations

## The Attempt at a Solution

I understand all the definitions for Integration, my problem lies with approaching the problem. Should I use first principles to solve the problem? or do I just need to quote the definition?

For example, can I say "since f(x) is constant then it must be the case that upper sums equal its lower sums. Which implies that its upper integral equals its lower integral. Therefore f is Riemann integrable. Such that [tex]\int ^{a}_{b}[/tex]f(x)dx = c(b-a)

Is this sufficient?

Thank you for your help.

M