The area (in sq units) of the region bounded by x=-1, x=2, y=x^2+1 and y=2 x-2 is

Step-by-step solution

Given curve is y=x^2+1 x^2=y-1 and line y=2 x-2 The intersection point of curve and line is aligned & x^2=2 x-2-1 & array l Now, x^2-2 x+3=0 Hence, there is no point of intersection array & Required area = _ -1 ^2 (y₂-y₁ ) d x & = _ -1 ^2 [ (x^2+1 )-(2 x-2) ] d x & = [ x^3 3 +x ]_ -1 ^2- [x^2-2 x ]_ -1 ^2 & = [ 8 3 +2- (- 1 3 -1 ) ]-[4-4-(1+2)] & = 14 3 + 4 3 -[-3] & =6+3=9 aligned