Improper Integration help
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Improper Integration help

[From: ] [author: ] [Date: 12-05-13] [Hit: ]
The answer, according to wolfram is pi/4.Simplified details: How do I find out what the infinity values are in order to obtain pi/4 as my final answer??-hint : tan ∞ = π / 2 and tan - ∞ = - π / 2-you certainly know that lim { t----> ∞ } of arctan ( t )= π / 2 ,ie.......
Integrate ((1)/(4x^2+4x+5)) from -infinity to +infinity.

Ive seperated both parts from (-infinity to -1/2) and (-1/2 to infinity) and I am getting (1/4)*(tan^-1((2x+1)/2)) as the integration...HOWEVER

I dont understand where to go from here. Basically I am asking for help on how to find out what values to put for -infinity and +infinity. The answer, according to wolfram is pi/4. But IDK how they are getting it as they dont show how they got the values for when the limit goes toward infinity

Simplified details: How do I find out what the "infinity" values are in order to obtain pi/4 as my final answer??

-
hint : tan "∞" = π / 2 and tan " - ∞ " = - π / 2

-
you certainly know that lim { t----> ∞ } of arctan ( t ) = π / 2 ,
ie. what angle has an infinite tangent ?....trig concept

Gads : I see I mistyped ! tan π / 2 = ∞ and tan ( - π / 2 ) = - ∞

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