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Math Help - Request feedback on basic integration concept

  1. #1
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    Request feedback on basic integration concept

    In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.

    (By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).

    The relevant part of the question asks to find the integral of (1-x)^(2) dx.

    But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.

    Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.

    For the integral of (1-x)^(2), I get
    integral (1 - 2x + x^(2))
    = x - x^2 + ((x^3)/3)

    while for the integral of (1 - x^(2)) I get
    x - (x^3)/3

    Again -- am I right, or is there some reason that for the purposes of integration,

    (1-x)^(2) = (1- x^(2)) ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lingyai
    In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.

    (By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).

    The relevant part of the question asks to find the integral of (1-x)^(2) dx.

    But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.

    Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.

    For the integral of (1-x)^(2), I get
    integral (1 - 2x + x^(2))
    = x - x^2 + ((x^3)/3)

    while for the integral of (1 - x^(2)) I get
    x - (x^3)/3

    Again -- am I right, or is there some reason that for the purposes of integration,

    (1-x)^(2) = (1- x^(2)) ?
    What you are doing looks right to me.

    RonL
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  3. #3
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    Thanks Cap'n
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by lingyai
    Thanks Cap'n
    Except of course for the constants of integration.

    RonL
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  5. #5
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    Thumbs up

    Understood
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