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March 29th, 2014, 07:13 AM   #1
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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!
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April 1st, 2014, 08:47 AM   #2
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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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