y=-2x^2, x=-2, y=0

If you mean the area bounded by y = -2x^2, x = -2, and y = 0:

• The x-range is from x = -2 to where the parabola meets y = 0, i.e., -2x^2 = 0 → x = 0.
• For x in [-2, 0], the vertical thickness is 0 − (−2x^2) = 2x^2.

Compute the area: A = ∫{-2}^{0} 2x^2 dx = (2/3) x^3 |{-2}^{0} = 0 − (−16/3) = 16/3.

So the area is 16/3 square units.