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Math Help - Riemann integral

  1. #1
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    Riemann integral

    Compute the Riemann integral of the absolute value of sinx from 0 to 2(pi)
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  2. #2
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    Quote Originally Posted by TexasGirl
    Compute the Riemann integral of the absolute value of sinx from 0 to 2(pi)
    We note that,
    f=|\sin x| is countinous thus it exists.
    If 0\leq x\leq \pi
    Then, f=\sin x by the definition of absolute value.
    If \pi \leq x\leq 2\pi
    Then, f=-\sin x by the definition of absolute value.
    Thus, by the subdivision rule,
    \int_0^{2\pi}|\sin x|dx=\int_0^{\pi}\sin xdx+\int_{\pi}^{2\pi} -\sin xdx
    I assume you can solve it from heir.
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  3. #3
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    yep...thanks
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