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hawkfalcon

  • 3 years ago

Calculus piecewise question

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  1. hawkfalcon
    • 3 years ago
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    \[f(x)=\left[\begin{matrix}x & x \le0 \\ x+1 & x>0\end{matrix}\right]\]

  2. hawkfalcon
    • 3 years ago
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    find \[\int\limits_{-2}^{1}xf(x)dx\]

  3. wio
    • 3 years ago
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    This is the discontinuous type of improper integral.

  4. anonymous
    • 3 years ago
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    break in two \[\int_{-2}^0+\int_0^1\]

  5. wio
    • 3 years ago
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    \[ \large \int\limits_{-2}^{1}xf(x)dx = \lim_{t\to 0^+} \int\limits_{-2}^{t}xf(x)dx + \lim_{t\to 0^-} \int\limits_{t}^{1}xf(x)dx \]

  6. hawkfalcon
    • 3 years ago
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    Okay, that makes sense. Just split into two.

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