Infinite interval - improper integrals, Mathematics

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Infinite Interval  - Improper Integrals

In this type of integral one or both of the limits that is upper limit and lower limit of integration are infinity.  In these cases the interval of integration is sopposed to be over an infinite interval.


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Sin[cot-1{cos(tan-1x)}], sin (cot -1 {cos (tan -1 x)}) tan -1 x = A  ...

sin (cot -1 {cos (tan -1 x)}) tan -1 x = A  => tan A =x sec A = √(1+x 2 ) ==>  cos A = 1/√(1+x 2 )    so   A =  cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s

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