3.95: Area between y=12x2y = 12 - x^{2} and y=x44x2+8y = x^{4} - 4x^{2} + 8

0606/13/O/N/25 — Question 8 · 7 marks

3.95 diagram
The diagram shows part of each of the curves y=12x2y = 12 - x^{2} and y=x44x2+8y = x^{4} - 4x^{2} + 8.
Find the area of the shaded region enclosed by y=12x2y = 12 - x^{2} and y=x44x2+8y = x^{4} - 4x^{2} + 8.
[7]