[tex]\it \int\limits^3_1 (|x+1|+|x-2|) dx [/tex]
Explicităm modulele:
[tex]\it |x+1| = x+1 ,\ \ \forall x\in [1, \ 3 ]
\\\;\\
|x-2| = -x +2 ,\ \ \forall x\in [1, \ 2 ]
\\\;\\
|x-2| = x -2 ,\ \ \forall x\in [2, \ 3 ] [/tex]
Integrala devine:
[tex]\it \int\limits^2_1 (x+1-x+2) dx + \int^3_2 (x+1+x-2) dx = \int\limits^2_1 3 dx+ \int^3_2 (2x-1) dx=
\\\;\\ \\\;\\
=3x\Big|^2_1 + (x^2-x)\Big|^3_2 = 6-3+6-2 = 7[/tex]
