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Thread: Evaluate the Integral

  1. #1
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    Evaluate the Integral

    Question : Evaluate the Integral

    $\displaystyle \int_{0}^{4} |x-2| dx$

    Solution
    My work::::::::::::::::::::::::::;;;;;;

    $\displaystyle \int_{0}^{4} |x-2| dx$ = $\displaystyle \int_{0}^{4} (x-2) dx$ = $\displaystyle \int_{0}^{4} x dx - \int_{0}^{4} 2 dx$ =.....= $\displaystyle 0$....................Is this correct???
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  2. #2
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    No, it's wrong, you can't remove the absolute value bars whenever you like.

    $\displaystyle |x-2|=x-2$ when? And $\displaystyle |x-2|=2-x$ when?
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  3. #3
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    Quote Originally Posted by zorro View Post
    Question : Evaluate the Integral

    $\displaystyle \int_{0}^{4} |x-2| dx$

    Solution
    My work::::::::::::::::::::::::::;;;;;;

    $\displaystyle \int_{0}^{4} |x-2| dx$ = $\displaystyle \int_{0}^{4} (x-2) dx$ = $\displaystyle \int_{0}^{4} x dx - \int_{0}^{4} 2 dx$ =.....= $\displaystyle 0$....................Is this correct???
    No, it's incorrect.

    $\displaystyle |x - 2| = x - 2$ for $\displaystyle x \geq 2$, and $\displaystyle |x - 2| = -(x - 2) = 2 - x$ for $\displaystyle x < 2$.

    So $\displaystyle \int_0^4{|x - 2|\,dx} = \int_0^2{2 - x\,dx} + \int_2^4{x - 2\,dx}$.
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  4. #4
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    thanks mite i have got the answer as 6.....
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  5. #5
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    Quote Originally Posted by zorro View Post
    thanks mite i have got the answer as 6.....
    Check your arithmetic.

    integrate |x - 2| from x = 0 to x = 4 - Wolfram|Alpha
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