Concept:Evaluate a definite integral by expressing the radical as a power, integrating term by term, then applying the limits.Explanation:Rewrite the cube root: 3x2=x2/3.So the integral becomes ∫01(4x−6x2/3)dx.Integrate each term:∫4xdx=2x2.∫−6x2/3dx=−6⋅5/3x5/3=−518x5/3.Thus the antiderivative is F(x)=2x2−518x5/3.Evaluate from 0 to 1:F(1)=2(1)2−518(1)5/3=2−518=−58.F(0)=2(0)2−518(0)5/3=0.So ∫01(4x−63x2)dx=−58−0=−58.Answer:−58 (Option B)