Lemma: An integration of a continuous function is zero iff function is identical zero

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In this lemma, if we have a nonnegative function over any finite closed interval whose integration is zero on that closed interval if and only if function is identical zero on that interval.
  1. ExExam
  2. Exexam
  3. integration of positive function is zero
  4. Lemma
  5. zero function
  6. integration of positive function
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