The area of the region bounded by the curve y = x² − x, the x-axis, x = 0 and x = 2 is:

The area of the region bounded by the curve y = x² − x, the x-axis, x = 0 and x = 2 is:

• A. 1 sq unit
• B. 5/6 sq unit
• C. 7/6 sq units
• D. 2 sq units

Answer: A) 1 sq unit

Explanation: Curve cuts x-axis at x = 0, 1. Area = ∫[0 to 1] |x² − x| dx + ∫[1 to 2] (x² − x) dx = ∫[0 to 1] (x − x²) dx + ∫[1 to 2] (x² − x) dx = [x²/2 − x³/3]₀¹ + [x³/3 − x²/2]₁² = (1/2 − 1/3) + [(8/3−2) − (1/3−1/2)] = 1/6 + [2/3 − (−1/6)] = 1/6 + 4/6 + 1/6 = 6/6 = 1 sq unit.