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Math Help - Integrate the following equation

  1. #1
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    Integrate the following equation

    Question : Integrate \int_{-1}^{1} |1- x| dx
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  2. #2
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    Quote Originally Posted by zorro View Post
    Question : Integrate \int_{-1}^{1} |1- x| dx
    Note that |1 - x| = 1 - x when x < 1 and | 1 - x| = -(1 - x) = x - 1 when x \geq 1.
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  3. #3
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    or note that the integrand is non-negative for -1\le x\le1, so the absolute value is irrelevant there and you can simply evaluate \int_{-1}^1(1-x)\,dx.
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    Quote Originally Posted by zorro View Post
    Question : Integrate \int_{-1}^{1} |1- x| dx
    \forall x\in [-1,1],1-x\geq 0
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  5. #5
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    Is this correct?

    Quote Originally Posted by Raoh View Post
    \forall x\in [-1,1],1-x\geq 0


    \int_{-1}^{1} |1-x|dx \ =  \int_{-1}^{1} (1-x)dx = ........ = 2

    Is this correct???
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  6. #6
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    Quote Originally Posted by zorro View Post
    \int_{-1}^{1} |1-x|dx \ =  \int_{-1}^{1} (1-x)dx = ........ = 2

    Is this correct???
    i believe you're right
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