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Prove that the integral diverge.

  1. Jul 4, 2011 #1
    Let f:[0,inf) [itex]\rightarrow[/itex] R+ (f is positive...).
    f is continuous and: [PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP350919g712a61ice7c02000046b8i2i10g466041?MSPStoreType=image/gif&s=15&w=87&h=35. [Broken]

    prove that :[PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP334719g7149aa8g6efha000027bhe3a6fe5cg8c9?MSPStoreType=image/gif&s=22&w=93&h=40 [Broken]

    where [PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP165019g717ia4c72gibe000039f8g9b652gd3664?MSPStoreType=image/gif&s=41&w=99&h=35. [Broken]

    some tips?
    thanks.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 4, 2011 #2

    HallsofIvy

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    You say that [itex]\int_0^\infty f(x) dx= \infty[/itex] and then [itex]g(x)= \int_0^\infty f(t)dt[/itex]. Did you mean [itex]g(x)= \int_0^x f(t)dt[/itex]?
     
  4. Jul 5, 2011 #3
    Yes, sorry for the mistake, this is exactly as you mentioned.
     
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