Find the area bounded by the parabola y^2 = 4x and the line y = 2x.
Answer and explanation
Correct answer: B. 1/3 square units
- Step 1: Intersection points: (2x)^2 = 4x => 4x^2 = 4x => 4x(x - 1) = 0 => x = 0 or x = 1.
- Step 2: For x ∈ [0, 1], parabola is above line: y_parabola = 2√x, y_line = 2x.
- Step 3: Area = ∫_(0 to 1) (2√x - 2x) dx = [2 * (2/3) x^(3/2) - x^2]_(0 to 1).
- Step 4: = 4/3 - 1 = 1/3 square units.
Why not the others: The alternative choices (2/3 square units, 1/6 square units, 4/3 square units) stem from algebraic sign mistakes, misapplying coordinate formulas, or intermediate arithmetic calculation slips.
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