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JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    Let \[f:R\to R\] be a function and satisfies \[f(2)=-1,f'(2)=4\]. If \[\int\limits_{2}^{3}{(3-x)f''(x)dx=7}\], then f[c] has the value equal to

    A)  10                               

    B)  9

    C)  8                                

    D)  5

    Correct Answer: A

    Solution :

    \[\int\limits_{2}^{3}{(3-x)\,f''(x)\,dx=7;}\] \[\Rightarrow \,\,(3-x).\,f'(x)|_{2}^{3}\,+\int\limits_{2}^{3}{f'(x)\,dx=7}\] \[\Rightarrow \,\,0-f'(2)+f(3)\,-f(2)=7\] \[\Rightarrow \,\,-4+f(3)+1\,=7\Rightarrow \,f(3)=10\]


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