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JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    If the integral \[\int{\frac{5\tan x}{\tan x-2}dx=x+a\,\ell n\left| \sin x-2\cos x \right|+k}\], then a is equal to:   AIEEE  Solved  Paper-2012

    A)              \[-1\]                                       

    B)              \[-2\] 

    C)              1                                                

    D)              2

    Correct Answer: D

    Solution :

                 \[\int{\frac{5\tan x}{\tan x-2}dx=\int{\frac{5\sin x}{\sin x-2\cos x}dx}}\] \[=\int{\frac{(\sin x-2\cos x)+2(\cos x+2\sin x)}{(\sin x-2\cos x)}dx}\] \[=\int{dx+2\int{\frac{\cos x+2\sin x}{\sin x-2\cos x}dx=x+2\ln }}\] \[\left| \sin x-2\cos x) \right|+k\]\[\Rightarrow \,\,\,a=2\]


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