The area (in sq. units) of the region A = x , y : y 2 2 ≤ x ≤ y + 4 is:

Step-by-step solution

We have to find the area of the region A = x ,   y : y 2 2 ≤ x ≤ y + 4 Now, to find the point of intersection of the curves x = y 2 2 and x = y + 4 , we equate the value of x , to get y 2 2 = y + 4 ⇒ y 2 = 2 y + 8 ⇒ y 2 - 2 y - 8 = 0 ⇒ y - 4 y + 2 = 0 ⇒ y = 4 or y = - 2 And, the graph of the given functions is as The shaded area is the required area, and Area = ∫ - 2 4 x l i n e - x p a r a b o l a d y = ∫ - 2 4 y + 4 - y 2 2 d y Now, using ∫ x n d x = x n