The following integral was on the qualifying test: Any ideas? I'm stumped.
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Originally Posted by Random Variable The following integral was on the qualifying test: Any ideas? I'm stumped. Let or ?
How about the following: let then solving for y then using the positive root since we're integrating over positive values of x ?
Last edited by Random Variable; January 28th 2010 at 10:14 PM.
then you solve for y using quadratic formula ? y= x/2 + sqrt(x^2 +4)/2 ? or am I way off base?
Originally Posted by Random Variable What about the following: let then ? Originally Posted by Calculus26 then you solve for y using quadratic formula ? y= x/2 + sqrt(x^2 +4)/2 ? or am I way off base? No no! That is correct. I didn't realize it was supposed to be an infinite surd . Yes, that method works...if you can prove that the surd converges . P.S. You can choose the according to the fact that for
Then since y > 0 we take y= x/2 + sqrt(x^2 +4)/2 ?
Originally Posted by Calculus26 Then since y > 0 we take y= x/2 + sqrt(x^2 +4)/2 ? I would agree with that. the answer is
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