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(Solved): Determine the upper and lower Darboux integrals for g(x)={x,0,ifxisrationalifxi ...


Determine the upper and lower Darboux integrals for \[ g(x)=\left\{\begin{array}{cc} x, & \text { if } x \text { is rational

Determine the upper and lower Darboux integrals for on . Is integrable or not? (Prove your answer, but it is OK if you simply state what and are. You don't need to prove them rigorously.)


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Step 1: If the function { ? x if x is rational 0 if x=is irrational ? on [0, b] is not integrable? To prove this, we need to show that the upper and lower Darboux integrals are not equal. Step 2: Let P be a partition of [0, b] such that 0=t 0 ?
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