Prove that the integral diverge.

[puzzek]

Let f:[0,inf) \rightarrow 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.

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

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

some tips?
thanks.

 

[HallsofIvy]

You say that \int_0^\infty f(x) dx= \infty and then g(x)= \int_0^\infty f(t)dt. Did you mean g(x)= \int_0^x f(t)dt?

 

[puzzek]

Yes, sorry for the mistake, this is exactly as you mentioned.