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Homework Help: Area Under Curves (Integrals)

  1. Apr 10, 2008 #1
    Suppose the area of the region between the graph of a positive continuous function f and the x-axis from x = a to x = b is 4 square units. Find the area between the area between the curves y = f(x) and y = 2f(x) from x = a to x = b.

    Attempt:

    Since 2 f(x) is greater than f(x) we can call it g(x) and that will be the dominant function.

    [tex]\int (g(x) - f(x)) dx[/tex]

    It becomes...
    [tex]G(x) - F(x)[/tex]

    What do I do next?

    Thanks
     
  2. jcsd
  3. Apr 10, 2008 #2
    You said g(x)=2f(x), so what can you say about the relation between G(x) and F(x) ..?

    Note that you want to consider definite integrals

    [tex]
    \int_a^b{dx(g(x)-f(x))}
    [/tex]

    Can you simplify g(x)-f(x)..?
     
  4. Apr 10, 2008 #3
    umm yeah i guess that took me off course.
     
  5. Apr 10, 2008 #4
    so then how would i do it?
     
  6. Apr 10, 2008 #5
    Uhm,

    g(x)-f(x) = 2f(x)-f(x) =...?
     
  7. Apr 10, 2008 #6
    Umm that equals f(x)
     
  8. Apr 10, 2008 #7
    very good, so
    [tex]\int_a^b{dx(g(x)-f(x))}=\int_a^b{dx(2f(x)-f(x))}=\int_a^b{dx(f(x))}=...=?[/tex]
     
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