2. Solved Papers
  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    If for every integer\[n,\int_{n}^{n+1}{f(x)}\,dx={{n}^{2}},\]then the value of\[\int_{-2}^{4}{f(x)}\,dx\]is

    A)  16           

    B)  14

    C)  19           

    D)  None of these

    Correct Answer: C

    Solution :

    Given,      \[\int_{n}^{n+1}{f(x)dx}={{n}^{2}}\] On putting \[n=-2,-1,0,1,2,3,\]we get \[\int_{-2}^{-1}{f(x)}\,dx=4\int_{-1}^{0}{f(x)}\,dx=1\] \[\int_{0}^{1}{f(x)}\,dx=0\int_{1}^{2}{f(x)}\,dx=1\] \[\int_{2}^{3}{f(x)}\,dx=4\int_{3}^{4}{f(x)}\,dx=9\] \[\therefore \] \[\int_{-2}^{4}{f(x)}\,dx=4+1+0+1+4+9=19\]


You need to login to perform this action.
You will be redirected in 3 sec spinner