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JEE Main & Advanced Sample Paper JEE Main Sample Paper-2

  • question_answer
    If \[\int\limits_{0}^{5}{(4a{{x}^{3}}+3b{{x}^{2}}+2cx+d)dx}\]\[=\int\limits_{2}^{5}{(4a{{y}^{3}}=3b{{y}^{2}}+2cy+d)dy}\] then \[4a+2b+c=\]

    A)  \[-\frac{d}{4}\]                               

    B)  \[-\frac{d}{2}\]

    C)  \[-d\]                                  

    D)  \[-2d\]

    Correct Answer: B

    Solution :

    \[\int\limits_{0}^{2}{(4a{{x}^{3}}+3b{{x}^{2}}+2cx+d)dx=0}\] \[\Rightarrow \] \[a\cdot {{2}^{4}}+b\cdot {{2}^{3}}+c\cdot {{2}^{3}}+d\cdot 2=0\] \[\Rightarrow \] \[16a+8b+4c+2d=0\] \[\Rightarrow \] \[4a+2b+c=-\frac{d}{2}\]


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