Really really need assistance and help. Thank you in advance..

Question

Use geometry to evaluate  where .

Answer 1

Try graphing the function to see if you can recognize what familiar geometric shape it forms.

Answer 2

The two components of the piecewise function, x + 4 when -4 ≤ x ≤ -1, and -x + 2 when -1 < x ≤ 2, define two line segments. Their intersection point occurs when x = -1 and y = x + 4 = -1 + 4 = 3. Since we're looking for the area between the curve and x-axis, our other points of interest are the x-intecepts. For the part of the graph defined by x + 4, this intercept is -4, and for the part defined by -x + 2, it's 2. Taking these three points (-4, 0), (-1, 3), and (2, 0).

These points form a triangle with a base of 2 - (-4) = 6 and a height of 3, so its area, and by extension