Question

Find the area bounded by curves {(x, y): y ≥ x² and y = |x| }.

Answer 1

y ≥ x² and y ≤ |x|

consider then as curves y = x² (upward parabola vertex (0, 0) 

y= |x| (line) 

As y ≥ x² , so area above parabola y ≤ |x|, so area below modulus 

∴ required area is shaded one 

= 2x [Area under line in 1^st quadrant) – (Area under parabola in 1^st quadrant)]