March 29th, 2014, 07:13 AM  #1 
Senior Member Joined: Apr 2012 Posts: 135 Thanks: 1  improper integral
i have the following integral: integral from 1 to pi/2 arcsinx/(x^2). The integral from 1 to 0 gives oo and from 0 to pi/2 +oo... what is the conclusion here? Or integral from 1 to 1 1/x is this equal with 0? because we have the same amount of "infinity" on both sides. It is necessary to solve the other side of the improper integral if the first one is divergent? And the last question: It is possible to have oo on one side , +oo on the other side and the integral to converge? Thank you! 
April 1st, 2014, 08:47 AM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions 
$$ \int^1_{1} \frac{1}{x} \, dx \neq 0 $$ because the integral actually diverges. The function has no antiderivative on the specified region. 

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improper, integral 
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