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JEE Main & Advanced Mathematics Definite Integration Question Bank Self Evaluation Test - Application of Integrals

  • 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 :

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


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