How to determine if the improper integral converges or diverges int 1/[sqrt x] from 0 to infinity?

Pieszkowo3gc4

Pieszkowo3gc4

Answered question

2023-03-17

How to determine if the improper integral converges or diverges 1 x from 0 to infinity?

Answer & Explanation

Haylee French

Haylee French

Beginner2023-03-18Added 7 answers

Although the integral in this instance is so straightforward to evaluate that we can just compute it and check if the value is bounded, we could use the comparison test for improper integrals.
0 1 x   d x = 0 x - 1 2 = [ 2 x ] 0 = lim x ( 2 x ) - 2 0 = lim x ( 2 x ) =
This means that the integral diverges.

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