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??
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 ) = - ∞
ie. what angle has an infinite tangent ?....trig concept
Gads : I see I mistyped ! tan π / 2 = ∞ and tan ( - π / 2 ) = - ∞
Report Abuse