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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

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

    A) \[f\left( x \right)=cos\left( 3x+4 \right)+3\left( x-1 \right)sin\left( 3x+4 \right)\]

    B) \[f\left( x \right)=sin\left( 3x+4 \right)+3\left( x-1 \right)cos\left( 3x+4 \right)\]

    C) \[f\left( x \right)=sin\left( 3x+4 \right)-3\left( x-1 \right)cos\left( 3x+4 \right)\]

    D) None of these

    Correct Answer: B

    Solution :

    [a] We have \[\int\limits_{1}^{b}{f\left( x \right)dx=\left( b-1 \right)sin\left( 3b+4 \right)}\] differentiate both side w.r.t. b \[f\left( b \right).1-0=\left( b-1 \right).3cos\left( 3b+4 \right)+sin\left( 3b+4 \right).1\]\[f\left( b \right)=3\left( b-1 \right)cos\left( 3b+4 \right)+sin\left( 3b+4 \right)\] \[f\left( x \right)=3\left( x-1 \right)cos\left( 3x+4 \right)+sin\left( 3x+4 \right)\]


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