Concept:The function x∣x∣ is odd, so its integral over [−1,1] is zero.Explanation:We evaluate ∫−11x∣x∣dx by splitting at x=0.For x<0, ∣x∣=−x, so x∣x∣=−x2.For x≥0, ∣x∣=x, so x∣x∣=x2.Thus, the integral becomes: ∫−10(−x2)dx+∫01x2dx.Integrate: −[3x3]−10+[3x3]01.Evaluate: −[0−(−31)]+[31−0]=−31+31=0.Alternatively, since x∣x∣ is an odd function, the integral over symmetric limits is zero directly.Answer:0 (Option A).