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

  • question_answer Area between the curve \[y=\cos x\] and \[x-\]axis when \[0\le x\] is [MP PET 1997]

    A)            2    

    B)            4

    C)            0    

    D)            3

    Correct Answer: B

    Solution :

                       \[y=\cos x\],   When \[x\in \left[ 0,\frac{\pi }{2} \right],\cos x\ge 0\]                            When \[x\in \left[ \frac{\pi }{2},\frac{3\pi }{2} \right],\cos x\le 0\]                            When \[x\in \left[ \frac{3\pi }{2},2\pi  \right],\cos x\ge 0\]            Thus required area is given by,            \[\int_{0}^{\pi /2}{\,\,ydx}=\int_{0}^{\pi /2}{\cos x\,dx+\int_{\pi /2}^{3\pi /2}{(-\cos x)dx+\int_{3\pi /2}^{2\pi }{\,\cos xdx}}}\]                      \[=1+2+1=4sq.\]unit.

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