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How to tell if an integral converges or diverges?

Integrate: 1 dx between 0 and Infinity

Lim b -> Infinity of [x] between 0 and b

Hence

Lim b -> Infinity

How am i supposed to know that this diverges?

Reply 1

RDKGames

Study Forum Helper

Original post by NoahMal

Integrate: 1 dx between 0 and Infinity

Lim b -> Infinity of [x] between 0 and b

Hence

Lim b -> Infinity

How am i supposed to know that this diverges?

The value of the integral is just

b

b

goes to infinity, so the value of the integral diverges to infinity.

Reply 2

NoahMal

Original post by RDKGames

The value of the integral is just

b

b

goes to infinity, so the value of the integral diverges to infinity.

Sorry for such a noob question but what is convergence and divergence aagain? Cant find any good sources

Reply 3

RDKGames

Study Forum Helper

Original post by NoahMal

Sorry for such a noob question but what is convergence and divergence aagain? Cant find any good sources

Not to use any technical terms, but you say some expression is convergent if it tends to a finite limit. We say it is divergent if it this not convergent.

So, what does

b

tend towards when

b \rightarrow \infty

... ?

This might be a bit of a bad example in your case to really understand what this means, so alternatively, decide whether the following expression is convergent or divergent: