Consider the function f ( x )=| x -1|+ x ^2 , where x R . What is the area of the region bounded by x -axis, the curve y=f(x) and the two ordinates x=1 and x= 3 2 ?

Step-by-step solution

Area required for given region is aligned A₂ & = ₁^ 3 / 2 f(x) d x & = ₁^ 3 / 2 [x^2+x-1 ] d x & = [ 1 3 x^3+ 1 2 x^2-x ]₁^ 3 / 2 A₂ & = ( 1 3 ( 27 8 )+ 1 2 ( 9 4 )- 3 2 )- ( 1 3 (1)+ 1 2 (1)-1 ) A₂ & = 11 12 square unit aligned