The area (in sq. units) bounded by (x^2=y, y=x+2 ) and the ( X )-axis is

Step-by-step solution

Indicate the region bounded by the curves (x^2=y, y=x+2 ) and (X )-axis and obtain the area enclosed by them. The parabola and line meet in points (P(-1,1) ) and (Q(2,4) ). The line cuts the axes in ((-2,0) ) and (B(0,2) ). Here, we have to find the area bounded by the curves and (X )-axis i.e. area (O R A P Q ) i.e. area (A P R+ ) area (P R O ) ( aligned & = _ -2 ⁻¹ y_ line d x+ _ -1 ^0 y_ parabola d x & = _ -2 ⁻¹(x+2) d x+ _ -1 ^0 x^2 d x & = [ x^2 2 +2 x ]_ -2 ⁻¹+ [ 1 3 x^3 ]_ -1 ^0 & = 1 2 + 1 3 = 5 6 sq units