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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\frac{{{\sin }^{2}}x-{{\cos }^{2}}x}{{{\sin }^{2}}x{{\cos }^{2}}x}dx=}\] [MP PET 1996]

    A)            \[\tan x+\cot x+c\]

    B)            \[\tan x+\text{cosec}\,x+c\]

    C)            \[-\tan x+\cot x+c\]

    D)            \[\tan x+\sec x+c\]

    Correct Answer: A

    Solution :

               \[\int_{{}}^{{}}{\frac{{{\sin }^{2}}x-{{\cos }^{2}}x}{{{\sin }^{2}}x{{\cos }^{2}}x}}\,dx=\int_{{}}^{{}}{{{\sec }^{2}}x\,dx-\int_{{}}^{{}}{\text{cose}{{\text{c}}^{\text{2}}}\,x\,dx}}\]                                                                     \[=\tan x+\cot x+c.\]


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