2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 15

  • question_answer
    If the integral \[\int_{{}}^{{}}{\frac{5\tan }{\tan x-2}dx=x+a\ln }\]\[|\sin x-2\cos x|+k\],then a is equal to

    A) 1         

    B) 2     

    C) - 1       

    D)        - 2

    Correct Answer: B

    Solution :

    [b]: \[\int_{{}}^{{}}{\frac{5\tan x}{\tan x-2}}dx=x+a\ln |\sin x-2\cos x|+k\] On differentiating both sides, we get \[\frac{5\tan x}{\tan x-2}=1+\frac{a(cos\,x+2sin\,x)}{\sin x-2\cos x}\] \[\Rightarrow \]\[\frac{5\sin x}{\sin x-2\cos x}=\frac{\sin x(1+2a)+cos\,x(a-2)}{\sin x-2\cos x}\] \[\Rightarrow \]\[a=2\]


You need to login to perform this action.
You will be redirected in 3 sec spinner