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If int_a^b f(x) dx = a+2b, then what is int_a^b (f(x) + 5) dx equal to

  1. Feb 14, 2005 #1
    If [tex]\int_{a}^{b} f(x)dx = a+2b[/tex] then [tex]\int_{a}^{b} (f(x)+5)dx = ?[/tex]

    Here's what I did:
    [tex]\int_{a}^{b} (f(x)+5)dx = \int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx [/tex]
    [tex]\int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx = a+2b + 5b - 5a[/tex]
    [tex]\int_{a}^{b} (f(x)+5)dx = 7b-4a[/tex]

    Did I do this correctly? I know the answer is correct but I want to know if my thought process was correct or not. Thanks
     
  2. jcsd
  3. Feb 14, 2005 #2

    dextercioby

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    It is very correct.

    Daniel.
     
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