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Question:

The area of the region bounded by the parabola (y²)² = x, the tangent to the parabola at the point (2, 3), and the x-axis is

3

6

9

12

Solution:

Equation of tangent at (2,3): 2y = x + 4
∫₀³[(y²)² + 1] − [2y] dy = ∫₀³[(y²)² − 2y + 4] dy = [(y³/3) − y² + 4y]₀³ = 9