The area common to the parabola y = 2x2 and y = x2 + 4 is

The area we need looks like –



We need to find the points of intersection to set the bounds of integration.


At points of intersection, y = x2 + 4 = 2x2


or, x2 – 4 = 0


(x + 2)(x – 2) = 0


x = -2, 2


The points of intersection are (-2, 8) and (2, 8), which is also evident from the graph.


So, the area A of the shaded region is –


A =


=


Since 4 – x2 is an even function,


A =


=


=


= 32/3 (Ans)

1