Prove that the integral diverge.

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The discussion focuses on proving the divergence of the integral of a positive continuous function f defined on the interval [0, ∞). The integral in question is expressed as ∫₀^∞ f(x) dx = ∞, with the correction noted that g(x) should be defined as g(x) = ∫₀ˣ f(t) dt. The participants clarify the mathematical notation and ensure the correct interpretation of the integral limits, emphasizing the importance of precise definitions in calculus.

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

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