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JEE Main & Advanced AIEEE Solved Paper-2010

  • question_answer
    Let\[p(x)\]be a function defined on R such that \[p'(x)=p'(1x),\]for all\[x\in [0,1],p(0)=1\]and\[p(1)=41.\] Then \[\int\limits_{0}^{1}{p(x)}dx\]equals -       AIEEE  Solved  Paper-2010

    A) \[\sqrt{41}\]

    B)                        21                          

    C)                        41                          

    D)        42

    Correct Answer: B

    Solution :

    \[P'(x)=P'(1x)\] integrate \[P(x)=P(1x)+k\]                              ------- (1) put\[x=1\] \[P(1)=P(0)+k\] \[41=1+k\] \[K=42\] Put in (1) \[P(x)=P(1x)+42\]                            ------(2) Now \[I=\int\limits_{0}^{1}{P(x)dx}\] also \[I=\int\limits_{0}^{1}{P(1-x)dx}\] \[2I=\int\limits_{0}^{1}{(P(x)+P(1-x))dx}\] using (2) \[2I=\int\limits_{0}^{1}{42}dx=42(x)_{0}^{1}\] \[I=21\]


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