The area (in square units) bounded by the curves y=2 x^2 and y= x-[x], x+|x| in between the lines x=0 and x=2 is

Step-by-step solution

aligned & y= x-[x], x+|x| & y= cases 2 x, & x 0 x , & x aligned & = | ₀^1 2 x d x- ₀^1 2 x^2 d x |+ | ₁^2 2 x^2 d x- ₁^2 2 x d x | & = | [ 2 x^2 2 ]₀^1- [ 2 x^3 3 ]₀^1 |+ | [ 2 x^3 3 ]₁^2- [ 2 x^2 2 ]₁^2 | & = |1- 2 3 |+ | 16 3 - 2 3 -4+1 |= 1 3 + 5 3 =2 sq. units. aligned