In a recent homework assignment, I was asked to prodive a definition for ∫f(x) in the Region D, provided there was a discontinuity somewhere in the region. To define the integral, we merely removed a sphere centered on the discontinuity of radius δ>0 and found the limit of the integral as δ→0.(adsbygoogle = window.adsbygoogle || []).push({});

My question is how would you provide a more generalized definition for a function that had multiple undefined points? if i had points (x1,y1) and (x2,y2) where the function was undefined.

Would I somehow split the integral up into three parts?

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# Multiple Integrals for Functions Unbounded at Isolated Points

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