JEE Main & Advanced Mathematics Definite Integration Question Bank Area Bounded by Region, Volume and Surface Area of Solids of Revolution

  • question_answer The ratio of the areas bounded by the curves \[y=\cos x\] and \[y=\cos 2x\] between \[x=0,\] \[x=\pi /3\] and \[x-\]axis, is                                                                       [MP PET 1997]

    A)            \[\sqrt{2}:1\]                       

    B)            \[1:1\]

    C)            \[1:2\]                                     

    D)            \[2:1\]

    Correct Answer: D

    Solution :

                       \[{{A}_{1}}=\int_{0}^{\pi /3}{\cos x\,dx=\frac{\sqrt{3}}{2}}\], \[{{A}_{2}}=\int_{0}^{\pi /3}{\cos 2x\,dx=\frac{\sqrt{3}}{4}}\]            \ \[{{A}_{1}}:{{A}_{2}}=2:1\].


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