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Math Help - Absolute value integration.

  1. #1
    Member integral's Avatar
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    Absolute value integration.

    Such as:

    \int^{2}_{0} \left | 2x \right |dx

    How do you solve this?
    Thank you in advance


    \int
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  2. #2
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    Quote Originally Posted by integral View Post
    Such as:

    \int^{2}_{0} \left | 2x \right |dx

    How do you solve this?
    Thank you in advance


    \int
    Remember that

    |X| = \begin{cases}\phantom{-}X\textrm{ if }X \geq 0\\-X\textrm{ if }X < 0\end{cases}.

    So if X = 2x

    |2x| =  \begin{cases}\phantom{-}2x\textrm{ if }X \geq 0\\-2x\textrm{ if }X < 0\end{cases}.


    In your case, since 0 \leq 2x \leq 2, that means |2x| = 2x.
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  3. #3
    Member integral's Avatar
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    So the indefinite would be the integral of positive 2x OR the integral of -2x?
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  4. #4
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    Quote Originally Posted by integral View Post
    So the indefinite would be the integral of positive 2x OR the integral of -2x?
    No, it's +2x only.
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