Improper Integral Problem (I just want to check my answer)

[jrmed13]

Homework Statement

integral (from 0 to 1) of (lnx)dx/(x^0.5)

Homework Equations

I did u-substitution and got the antiderivative to be 4ln(sqrt(x)) - 4sqrt(x)

The Attempt at a Solution

The answer that I got was that the limit of the antiderivative (as t approaches 0 from the right; bounds are 1, t) was infinity, so the integral is divergent.

I just want to check my answer and see if it is correct. (I have an exam today)
Thanks!

 

[Mark44]

Homework Statement

integral (from 0 to 1) of (lnx)dx/(x^0.5)

Homework Equations

I did u-substitution and got the antiderivative to be 4ln(sqrt(x)) - 4sqrt(x)

The Attempt at a Solution

The answer that I got was that the limit of the antiderivative (as t approaches 0 from the right; bounds are 1, t) was infinity, so the integral is divergent.

I just want to check my answer and see if it is correct. (I have an exam today)
Thanks!

Nope. Your antiderivative is wrong. It should be 4sqrt(x)*ln(sqrt(x)) - 4sqrt(x). And the value of the integral (taking the lower limit as t --> 0+) is -4.