I want the answer of this question This is area under graph from inequality..

u need to draw the graphs of y= x+2 and y= x^2 and then mark the common region satisfying the inequality, which shall turn out to be the area enclosed between these 2 curves. now, we know that area enclosed between 2 curves f(x) and g(x) from x= a to x= b is given by ∫ (f(x) – g(x))dx from a to b.

so, as y= x+2 and y= x^2 intersect at x= – 1 and 2, we have the area A as:

A= ∫((x + 2) – (x^2))dx from – 1 to 2

= x^2/2 + 2x – x^3/3 | from – 1 to 2

= 9/2= 4.5 sq units