WAEC Further Mathematics 2022 Objective — Question 10

Question 10 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2022 Objective paper, with the correct answer and a full explanation.

Evaluate ∫₀¹ x²(x³+2)³ dx.

A. 56/12
B. 65/12Correct
C. 12
D. 65

Explanation

Let u=x³+2, du=3x²dx. The integral becomes ∫u³/3 du = [u⁴/12], evaluated from x=0 to 1: [(1+2)⁴−(0+2)⁴]/12 = (81−16)/12 = 65/12.

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