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

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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!!
 

Answers and Replies

  • #2
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6,736

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.
 

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