Question

find the area of the region bounded by y=1-2x^2 and y=|x|

Answer 1

the region is symmetric, and the curves intersect at (1,1)
a = 2∫[0,1] (2-x^2)-x dx = 7/3

Answer 2

or, using horizontal strips of width dy, you need to switch curves at (1,1)
a = 2(∫[0,1] y dy + ∫[1,2] √(2-y) dy) = 2(1/2 + 2/3) = 7/3