# Comparison Test on Interval 0 to 1

• theRukus
In summary, the question is asking to determine if the improper integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not. The solution involves using limits to evaluate the integral and determining if the limit exists or is infinite. The function is undefined at one of the interval endpoints and the limit must be evaluated from the other endpoint towards that point.

## Homework Statement

Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not.

## The Attempt at a Solution

I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming they want to know whether the function converges or diverges as x=>0, correct?

theRukus said:

## Homework Statement

Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not.

## The Attempt at a Solution

I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming they want to know whether the function converges or diverges as x=>0, correct?
Since this is an improper integral (the integrand is undefined at one of the interval endpoints), you need to use limits to evaluate the integral. If the limit below exists, the integral converges. If the limit doesn't exist or is infinite, the integral diverges.

$$\lim_{b \to 0^+}\int_b^1 \frac{5ln(x)dx}{x^{3/2}}$$

look for lnx ,x>1 but u should attention that its ln definition but when we solve that integral from 0 to 1 we want to account a surface from 0 to 1 so u should draw ln x it definition from 0 to 1 and when u draw that u know that. i hope that u understand my reason