Answer:
d. 4
Step-by-step explanation:
We want to evaluate
[tex] \int _{0} ^{4} |x - 2| dx[/tex]
geometrically.
The graph of
[tex]y = |x - 2| [/tex]
is a V-shaped graph with vertex at (2,0).
Geometrically, we want to find the area under this curve from x=0 to x=4.
This V-shaped graph formed two congruent triangles as shown in attachment.
The area of the triangle with height 2 units and base 2 units is
[tex] = \frac{1}{2} bh[/tex]
[tex] = \frac{1}{2} \times 2 \times 2[/tex]
[tex] = 2 \: square \: units[/tex]
Since the triangles are two we multiply by 2 to get:
[tex] = 4 \: square \: units[/tex]
