Find the area bounded by the parabolas y2 = 5x + 6 and x2 = y.

To get A & B solve y² = 5x + 6 & x² = y

⇒ A ≡ (–1, 1) & B ≡ (2, 4)

Required Area = Shaded Area

$=\int\limits_{-1}^2(\sqrt{5x+6}-x^2)dx=\frac{81}{15}=\frac{27}{5}$