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Math Help - integral abs values

  1. #1
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    integral abs values

    For all real b, the integral from 0 to b of the abs(2X) dx is

    A) -b *abs(b)
    B) b^2
    C) -b^2
    D) b*abs(b)
    E)none of the above
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by sandiego234 View Post
    For all real b, the integral from 0 to b of the abs(2X) dx is

    A) -b *abs(b)
    B) b^2
    C) -b^2
    D) b*abs(b)
    E)none of the above
    Page three I think

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  3. #3
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    Hello,

    Remember : if x<0, |x|=-x and if x>0, |x|=x.


    If b>0 :

    \int_0^b |2x| dx=\int_0^b 2x dx since x is in [0,b], positive values.

    =2 \cdot \frac{b^2}{2}=\boxed{b^2}


    Now, if b<0 :

    \int_0^b |2x|dx=\int_0^b -2x dx since x is in [b,0], negative values.

    =\int_b^0 2x dx

    =2 \cdot (\frac{0^2}{2}-\frac{b^2}{2})=\boxed{-b^2}

    So it's none of these...
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