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My exam is tomorrow and I don't understand this concept. Someone please help!


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What concept is troubling you? You did note the reversed limits of integration at the end, right? – hardmath Apr 18 '12 at 23:42
up vote 5 down vote accepted

Integrals have the properties that they are additive, constants can "jump out", and changing the sign can is the same as switching the limits. Namely:

  1. $\displaystyle\int_a^b(cf+g) = c\int_a^b f+\int_a^b g$
  2. $\displaystyle\int_a^b f = -\int_b^a f$

From these two properties the question should be clearer.

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Thank you. This did make it clearer. – David Apr 18 '12 at 23:50
@David, my pleasure. Good luck tomorrow. – Asaf Karagila Apr 18 '12 at 23:51

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