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Help riemann integral

Hi i don't understand this Riemann Integral i don't understand why we have to introduce a j, could someone explain this to me and as you can see from the picture i don't understand why the summation goes to zero because of the introduction of j
(edited 11 years ago)
Captureriemann.PNG73.7KB
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BabyMaths
f(x)=1 at one point in just one of the intervals and 0 everywhere in all the others

so U(f,Pn) is a load of zeros and a one all multiplied by 1/n. That is U(f,Pn)=1/n
Original post by ajayhp
Hi i don't understand this Riemann Integral i don't understand why we have to introduce a j, could someone explain this to me and as you can see from the picture i don't understand why the summation goes to zero because of the introduction of j


It's just separating a particular value in {1,2⋯n}\{1,2 \cdots n\} from the rest of the values. For these other values x≠2x\neq \sqrt{2} since x∉[1+j−1n,1+jn]x\not\in \left[1+\dfrac{j-1}{n},1+\dfrac{j}{n}\right] but 2∈[1+j−1n,1+jn]\sqrt{2}\in \left[1+\dfrac{j-1}{n},1+\dfrac{j}{n}\right] so necessarily f(x)=0f(x)=0 on those intervals.

Edit: beaten to it!
(edited 11 years ago)

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