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The area (in sq. units) of the region, given by the set {(x, y) ∈ R × R | x ≥ 0, 2x² ≤ y ≤ 4 − 2x} is:
- 8/3
- 17/3
- 13/3
- 7/3
Correct answer: 7/3
Solution
The area is calculated by finding the points of intersection of the curves defined by the inequalities and integrating the difference between the upper and lower bounds of y over the specified range of x. In this case, the area between the curves 2x² and 4 - 2x from x=0 to x=2 results in a total area of 7/3 square units.
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