Evaluate lim ||δ|| → 0 ∑ᵢ₌₁ⁿ cᵢ² 4/δxᵢ in the form of a definite integral.

a) ∫₀¹ 4cᵢ² dx
b) ∫₀¹ 4cᵢ²/xᵢ dx
c) ∫₀¹ 4cᵢ²/√xᵢ dx
d) ∫₀¹ 4cᵢ²/δxᵢ dx