Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 17

x=2y^2, x=4+y^2
2y^2=4+y^2
2y^2-y^2=4
y^2=4
y=+-2
Refer the attached image. Graph of x=2y^2 is plotted in red color and graph of x=4+y^2 is plotted in blue color.
Area of the region enclosed by the curves A=int_(-2)^2((4+y^2)-2y^2)dy
A=2int_0^2(4-y^2)dy
A=2[4y-y^3/3]_0^2
A=2(4*2-2^3/3)
A=2(8-8/3)
A=2((24-8)/3)
A=32/3