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Integration by substitution

  1. Jun 26, 2011 #1
    Hello! My problem is the following:

    Is

    [itex]\int_a^b f(z) dt = \int_{g(a)}^{g(b)} f(z) \frac{1}{g} dz[/itex]

    ?

    [itex]\frac{dz}{dt} = g [/itex]

    Thank you!
     
  2. jcsd
  3. Jun 26, 2011 #2

    hunt_mat

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    No. Is z a function of t?
     
  4. Jun 26, 2011 #3

    HallsofIvy

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    If z is a an invertible function of t such that dz/dt= g(t), then dz= g(t)dt, dt= (1/g(t))dz, but you cannot have g(t) in the integral with respect to z.
     
  5. Jun 26, 2011 #4
    z is a function of t, but not explicit, actually

    [itex] V_z = \frac{dz}{dt} [/itex]

    was the relation from which we took [itex] d t = \frac{dz}{V_z} [/itex].

    [itex] V_z = cte [/itex]
     
    Last edited: Jun 26, 2011
  6. Jun 26, 2011 #5
    My biggest problem with this question is [itex] f(z) [/itex] in both sides of the equation... and how do I change the integral from left side to the right.
     
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