JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\sec x\ dx=}\] [MP PET 1988, 95; RPET 1996]

    A)            \[\log \tan \left( \frac{\pi }{8}+\frac{x}{2} \right)+c\]

    B)            \[-\log (\sec x-\tan x)+c\]

    C)            \[\log (\sec x-\tan x)+c\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[\int_{{}}^{{}}{\sec x\,dx}=\log (\sec x+\tan x)+c\]                     \[=\log \left( \frac{1}{\sec x-\tan x} \right)+c=-\log (\sec x-\tan x)+c\].


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