How to Find the area A enclosed by the graphs of the given functions:

Question

f(x)=√(x), g(x)=x^2?

Answer 1

The functions are f (x ) = √x  and g (x) = x ²

To find the area enclosed by the graphs of given functions.

To find the limits where does the f (x ) = √x and g (x ) = x ² graphs intersects.

Graph

From the graph the functions f(x) and g(x) are intersection points 0 or 1.

To find area need to definite integration on linterval [0 ,1]

Area enclosed by the graphs of the functions f (x ) = √x and g (x ) = x ²is A  = 1/3 squre units.

Answer 2

The graphs intersect at f(x) = g(x).
 

Because f(x) ≥ g(x) for 0 ≤ x ≤ 1 find the area enclosed by the graphs as:
 

Area enclosed by the graphs is 1/3 square units.