The area bounded by the curve y = x|x|, the x-axis and the lines x = −1 and x = 1 is:

The area bounded by the curve y = x|x|, the x-axis and the lines x = −1 and x = 1 is:

• A. 2/3 sq unit
• B. 1/3 sq unit
• C. 0 sq unit
• D. 4/3 sq units

Answer: A) 2/3 sq unit

Explanation: Area = ∫[−1 to 0] (−x²) dx + ∫[0 to 1] (x²) dx (taking absolute value of area) = [−x³/3]₋₁⁰ + [x³/3]₀¹ = (0 − 1/3) + (1/3 − 0) = 1/3 + 1/3 = 2/3 sq unit.