Find the total area enclosed between the parabola y = x^2 and the line y = 2*x.
Answer and explanation
Correct answer: D. 4/3
- Step 1: Find intersection points: x^2 = 2x, so x(x - 2) = 0, giving x = 0 and x = 2.
- Step 2: On [0, 2], the line lies above the parabola: 2*x >= x^2.
- Step 3: Area = int_0^2 (2*x - x^2) dx = [x^2 - x^3 / 3]_0^2.
- Step 4: Evaluate at limits: (2^2 - 2^3 / 3) - 0 = 4 - 8/3 = 4/3.
Answer
4/3.
Why not the others: 2/3 evaluates (1/2)*(4/3); 2 evaluates 4 - 2; 8/3 evaluates 8/3 - 0.
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