Find the area of the region.

Question

y = 6 − 3x²,    y = 3x²,         −2 ≤ x ≤ 2

Answer 1

6 - 3x² = 3x²; x² = 1; x = ±1

From symmetry area A = 2(∫₀¹(6 - 6x²)dx + ∫₁²(6x² - 6)dx) = 2((6x - 2x³)₀¹ + (2x³ - 6x)₁²) = 8 + 8 + 8 = 24