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Is there an error in this problem?

  1. Aug 30, 2011 #1
    I am currently working on problem 32-15 in Calculus by Spivak, and in question (b)

    in the bottom line there is a relation
    [itex][\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]+[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0[/itex]

    But I can only get it to work out if

    [itex][\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]-[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0[/itex]

    as this would make sense since

    [itex]\int_a^b \phi_1''(x)\phi_2(x)-\phi_2''(x)\phi_1(x) + \phi_1'(x)\phi_2'(x)-\phi_1'(x)\phi_2'(x) dx = \int_a^b (\phi_1'(x)\phi_2(x))' dx - \int_a^b (\phi_2'(x)\phi_1(x))' dx[/itex]

    which would make it natural to conclude that the relation above is >0, since the above integral has been shown to be >0.

    .. Mads
  2. jcsd
  3. Aug 31, 2011 #2


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    I hard to guess what's going on here.

    What is the problem as stated in the textbook, and where are you stuck?
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