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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)