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KVPY Sample Paper KVPY Stream-SX Model Paper-9

  • question_answer
    The area bounded by the curves\[y=f(x),\]the x-axis and the ordinates \[x=1\]and \[x=b\]is \[(b-1)sin\,(3b+4).\]then\[f(x)\] is

    A) \[(x-1)\,cos\,(3x+4)\]

    B) \[\sin \,(3x+4)\]

    C) \[\sin \,(3x+4)+3(x-1)\,cos\,(3x+4)\]

    D) None of these

    Correct Answer: C

    Solution :

    \[ATQ\int_{1}^{b}{f(x)dx=(b-1)sin(3b+4)}\] Differentiating both sides w.r.t.b we get\[f(b)=3\left( b-1 \right)\cos \left( 3b+4 \right)+\sin \left( 3b+4 \right)\]\[\Rightarrow f(x)=3(x-1)cos(3x+4)+\sin \left( 3x+4 \right)\]


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