- #1
schniefen
- 178
- 4
- Homework Statement
- For a bounded, continuous and monotonous function on a half-open interval ##(a,b]##, how does one check if the function is integrable? (specifically Darboux integrable)
- Relevant Equations
- My definition of Darboux integrable: ##U(f,P)-L(f,P)<\epsilon## for all ##\epsilon>0##
For a closed interval ##[a,b]## I have learned that ##U(f,P)-L(f,P)=\frac{(f(b)-f(a))\cdot(b-a)}{N}## where ##N## is the number of subintervals of ##[a,b]## (if ##f## is monotonically decreasing, change the numerator of the fraction to ##f(a)-f(b)##). However, if the interval is half-open, then ##f(a)## is no longer defined. How does one go about this issue?