skippenmydesig
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We only have the epsilon-delta definition to work with for these.
Prove that f is integrable and verify the value. On [0,1] f(x)=1 if x=1/2 else 0. $$\int_{0}^{1} \,f$$ =0
Prove: If f is integrable on [0,1] then $$\lim_{{n}\to{\infty}}\ \frac{1}{n} \sum_{k=1}^{n} f(\frac{k}{n})$$ = $$\int_{0}^{1} \,f$$ .
Prove that f is integrable and verify the value. On [0,1] f(x)=1 if x=1/2 else 0. $$\int_{0}^{1} \,f$$ =0
Prove: If f is integrable on [0,1] then $$\lim_{{n}\to{\infty}}\ \frac{1}{n} \sum_{k=1}^{n} f(\frac{k}{n})$$ = $$\int_{0}^{1} \,f$$ .