Let f (x) = 1 if 2<=x<4(adsbygoogle = window.adsbygoogle || []).push({});

2 if x =4

-3, if 4<x<=7

Prove that this function is integrable on [2,7], state its value and prove that it is what you say it is.

Obviously integral of f from [2,7] is -7. but its proof and the integrability have me and my friends snagged.

Suggestions anyone?

SO far we have the idea that we have to prove that U(f,P) - L(f,P) , Epsilon

We computed that U(f,P) - L(f,P) =5 (Tj - Tj-1) where Tj and Tj-1 is the subinterval in which Tj-1<2<Tj. However we are stuck from here.

My notation is from a book called Calculus by Spivak. Basically U(f,P) is the upper sum and L(f,P) is th lwoer sum for a partition P of the interval. P = {A=T0,T1,T2,...,TJ-1,TJ,...TN=B}and A and B are the endpoints of hte interval.

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# Homework Help: Integrability of a step function

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