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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    For which of the following values of\[m\], is the area of the region bounded by the curve \[y=x-{{x}^{2}}\] and the line \[y=mx\] equals\[9/2\].

    A) \[-4\]                                    

    B) \[3\]

    C) \[2\]                                     

    D) \[4\]

    Correct Answer: D

    Solution :

    Area\[=\int_{0}^{1-m}{(x-{{x}^{2}}-mx)dx}\]                 \[=\left[ (1-m)\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3} \right]_{0}^{(1-m)}\]                 \[={{(1-m)}^{3}}\left( \frac{1}{2}-\frac{1}{3} \right)=\pm \frac{9}{2}\](given) Taking\[+ive\]sign\[{{(1-m)}^{3}}=27\Rightarrow m=-2\] Taking\[-ive\]sign\[{{(1-m)}^{3}}=-27\Rightarrow m=4\]


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