Wednesday, 27 April 2016

calculus - Nonsensical result in the midst of calculating an integral via substitution.




I was just calculating an integral via a trigonometric substitution and ended up with something pretty nonsensical but reversing the substitution seemed to clean it up.
π20dθ3+5cosθ t=tanθ2= 14log|2+t2t||0  =14log|2+tanθ22tanθ2||π20
Why is that the case? Is it something to do with the nature of the substitution?
Is there something I'm not considering when performing the substitution?



Any help would be much appreciated.



Thank you.




Edit: It turns out that tanπ4=1. Problem solved!


Answer



When θ goes from 0 to π2, θ2 goes from 0 to π4 so tanθ2 goes from 0 t0 1, not 0 to .


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