Question

Calculus piecewise question

Answer 1

\[f(x)=\left[\begin{matrix}x & x \le0 \\ x+1 & x>0\end{matrix}\right]\]

Answer 2

find \[\int\limits_{-2}^{1}xf(x)dx\]

Answer 3

This is the discontinuous type of improper integral.

Answer 4

break in two
\[\int_{-2}^0+\int_0^1\]

Answer 5

\[ \large
\int\limits_{-2}^{1}xf(x)dx = \lim_{t\to 0^+} \int\limits_{-2}^{t}xf(x)dx + \lim_{t\to 0^-} \int\limits_{t}^{1}xf(x)dx
\]

Answer 6

Okay, that makes sense. Just split into two.