The area (in sq. units) of the region bounded by y-x=2 and x^2=y is equal to

Step-by-step solution

array ll & y-x=2 and x^2=y & x^2-x-2=0 & (x-2)(x+1)=0 & x=2 or x=-1 & y=4, y=1 array Points of intersection of the two curves are - (2,4) and (-1,1) aligned Required area & = _ -1 ^2(2+x)-x^2 d x & =2[x]_ -1 ^2+ 1 2 [x^2 ]_ -1 ^2- 1 3 [x^3 ]_ -1 ^2 & =6+ 3 2 -3= 9 2 sq. units aligned