2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-2

  • question_answer
    \[\int_{{}}^{{}}{{{(\cos x)}^{\sin x}}(\ell n{{(\cos x)}^{\cos x}}-\tan x\cdot \sin x)dx=}\]

    A)  \[{{(\cos x)}^{\sin x}}.\ell n(\cos x)+c\]

    B)  \[{{(\cos x)}^{\cos x}}.\sin x+c\]

    C)  \[{{(\cos x)}^{\sin x}}+c\]

    D)  \[{{(\cos x)}^{\sin x-1}}+c\]

    Correct Answer: C

    Solution :

    \[{{(\cos x)}^{\sin x}}=t\] i.e., \[{{e}^{\sin x\ell n(\cos x)}}=t\] \[{{(\cos x)}^{\sin x}}\cdot \left( \ell n{{(\cos \,x)}^{\cos x}}-\tan x\sin x \right)dx=dt\] \[\int_{{}}^{{}}{dt=t+c}\]


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