(a) Using integration by substitution or otherwise, find ∫ x(2x² + 3)⁴ dx.

(b) (i) Sketch the curves y = x² and y = 4x - x² on the same axes, indicating clearly their points of intersection.
(ii) Find the area of the region enclosed between the curves y = x² and y = 4x - x².

(c) Given that ∫₀ᵏ (6x² + 2x) dx = 36, find the value of the constant k.

Question

(a) Using integration by substitution or otherwise, find ∫ x(2x² + 3)⁴ dx.

(b) (i) Sketch the curves y = x² and y = 4x - x² on the same axes, indicating clearly their points of intersection.
    (ii) Find the area of the region enclosed between the curves y = x² and y = 4x - x².

(c) Given that ∫₀ᵏ (6x² + 2x) dx = 36, find the value of the constant k.

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