11.3.2 Convolution of functions

Problem: Find the convolution of the functions \( f(x) \) and \( g(x) \), if the function \( f(x) \) takes a value, equal to zero, when \( x \notin[-1,4] \), and when \( x \in[-1,4] \) its graph consists of links of the broken-line \( A B C D \) : \[ \begin{array}{l} A(-1,0), B(1,2), C(2,-2), D(4,-2), \\ g(x)=\left\{\begin{array}{cc} 0, & x<0 \\ 1, & 0 \leq x<1 \\ 0, & x \geq 1 \end{array}\right. \end{array} \]