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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    \[\int\limits_{0}^{10}{f(x)dx=5,}\] then \[\sum\limits_{k=1}^{10}{\int\limits_{0}^{1}{f(k-1+x)\,\,dx}}\] equal to-

    A) 50

    B) 10

    C)    5

    D) None

    Correct Answer: C

    Solution :

    \[k-1+x=t,\]\[dx=dt\] \[\sum\limits_{k=1}^{10}{\int_{k-1}^{k}{f(t)dt=\int\limits_{0}^{1}{+\int\limits_{0}^{2}{+....+\int\limits_{9}^{10}{=\int\limits_{0}^{10}{f(t)\,\,dt=5}}}}}}\]


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