Find the area common to the parabola x = -2y2 and x = 1 - 3y2.

8/3 16/3 4/3 20/3

4/3

Required Area = 2 × shaded area = $2\int\limits_0^A[(1-3y^2)-(-2y^2)]dy$ Solve x = -2y2 & x = 1 - 3y2 ⇒ A ≡ (-2, 1) ⇒ Required Area = $2\int\limits_0^1(1-y^2)dy=4/3$