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Homework Help: Value of integration

  1. Nov 18, 2011 #1
    1. The problem statement, all variables and given/known data
    If [tex] f(x) = x^2 - x - \int_0^1 f(x) dx [/tex], find [tex]\int_0^2f(x) dx[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I found [tex]\int_0^2f(x) dx = \frac{2}{3} - 2 \int_0^1 f(x) dx[/tex]

    Is it possible the answer in numerical value? If yes, please guide me. Thanks
  2. jcsd
  3. Nov 18, 2011 #2
    Yes, it is. In fact, you can find the integral of f from 0 to 1 just by integrating both sides of the equation defining f.
  4. Nov 18, 2011 #3


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    Homework Helper

    The definite integral is a number: [tex]\int_0^1{f(x)dx}=A[/tex]
    The first equation can be written as [tex]f(x)=x^2-x-A[/tex].
    Integrate it from x=0 to x=1: you get an equation for A.

  5. Nov 18, 2011 #4


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    Homework Helper

    I managed to get something slightly prettier by writing
    [tex]\int_0^2 f(x) dx = I + \int_1^2 (x^2 - x - I) dx[/tex]
    [tex]I = \int_0^1 f(y) dy[/tex]
    is a constant.
  6. Nov 18, 2011 #5
    Ah I get it. Integrating f(x) from 0 to 1 never crosses my mind. Thanks a lot
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