KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • question_answer
    The area bounded by the curve \[y=x{{(3-x)}^{2}},\] the x-axis and the ordinates of the maximum and minimum points of the curve, is given by

    A) 1 sq. unit

    B) 2 sq. unit

    C) 4 sq. unit          

    D) none of these

    Correct Answer: C

    Solution :

    clearly, the curve \[y=x{{(3-x)}^{2}}\] has maximum at \[x=1\] and minimum at \[x=3.\]
    \[\therefore \]Req. area \[=\int_{1}^{3}{x{{(3-x)}^{2}}dx}\]
    \[=\left[ \frac{{{x}^{4}}}{4}-2{{x}^{3}}+\frac{9{{x}^{2}}}{2} \right]_{1}^{3}=4sq\,unit.\]

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