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 2 and x=1 ?

Step-by-step solution

f(x)= cases x^2+x-1 & x 1 x^2-x+1 & x 1 cases x R Hence area required for given region is aligned A₁ & = _ 1 / 2 ^1 f(x) d x & = _ 1 / 2 ^1 (x^2-x+1 ) d x & = [ 1 3 x^3- x^2 2 +x ]_ 1 / 2 ^1 & = ( 1 3 1- 1 2 +1 )- ( 1 3 1 8 - 1 2 1 4 + 1 2 ) A₁ & = 5 12 square unit. aligned