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Thread: Definite Integration: int[3,9][f(x)]dx = 7; find int[3,9][2*f(x) + 1]dx

  1. #1
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    Definite Integration: int[3,9][f(x)]dx = 7; find int[3,9][2*f(x) + 1]dx

    Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
    Evaluate
    ∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx

    Have no idea where to start

  2. #2
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    Quote Originally Posted by sojeee View Post
    Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
    Evaluate
    ∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx

    Have no idea where to start
    Start with:
    [tex]\displaystyle{\int [a * f(x)]dx \ = \ a * \int f(x)dx}[/tex]
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    Quote Originally Posted by Subhotosh Khan View Post
    Start with:
    [tex]\displaystyle{\int [a * f(x)]dx \ = \ a * \int f(x)dx}[/tex]

    Could u please explain this

  4. #4
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    Quote Originally Posted by sojeee View Post
    Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
    Evaluate
    ∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx
    Have no idea where to start
    I find your lack of grouping symbols makes this hard to read.
    If this is a correct reading then: [tex]\large{\int_3^9 {(2f(x) + 1)dx} = 2\int_3^9 {f(x)dx + } \int_3^9 {1dx} }[/tex]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  5. #5
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    Quote Originally Posted by sojeee View Post
    Could u please explain this
    You can factor out any constant in front of the integral sign!
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

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