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Function given as integral

  1. Oct 28, 2013 #1
    Suppose you are given a function:

    g(y) = ∫abf(x,y)dx
    And you are told f(x,c)=0. Does this then imply that:
    g(c)=∫abf(x,c)dx=∫0dx = 0
    Or are you supposed to calculate g(y) from the integral first and then plug in c to find g(c)?
     
  2. jcsd
  3. Oct 28, 2013 #2

    Mark44

    Staff: Mentor

    Your shortcut looks fine to me.
     
  4. Oct 29, 2013 #3
    But what if the you had something like:
    ∫f(x,t)tdx
    And f(x,a)=0. But the integration would yield something that cancelled t?
     
    Last edited: Oct 29, 2013
  5. Oct 29, 2013 #4

    arildno

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    Science Advisor
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    Gold Member
    Dearly Missed

    No, not unless the product function with f is sufficiently nasty.
    REMEMBER that you are basically adding together the areas of tiny rectangles of height f(x,a)*a in your new case.

    If f(x,a)=0 for all those rectangles, then the sum is zero.

    IF, however, you had something under the integral sign:
    f(x,t)/(t-a), then even though f(x,a)=0, you cannot conclude that f(x,a)/(a-a)=0, or is even defined.
     
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