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hawkfalcon
Calculus piecewise question
\[f(x)=\left[\begin{matrix}x & x \le0 \\ x+1 & x>0\end{matrix}\right]\]
find \[\int\limits_{-2}^{1}xf(x)dx\]
This is the discontinuous type of improper integral.
break in two \[\int_{-2}^0+\int_0^1\]
\[ \large \int\limits_{-2}^{1}xf(x)dx = \lim_{t\to 0^+} \int\limits_{-2}^{t}xf(x)dx + \lim_{t\to 0^-} \int\limits_{t}^{1}xf(x)dx \]
Okay, that makes sense. Just split into two.