Find the area of the region bounded by the given curves:

Question

f(x)=x and g(x)=x^3

Answer 1

The  given  fuctions  f(x) = x  and  g(x) = x³

The curves intersect at the points(0, 0) and (1,1).

x³< x

The area between them bounded by the horizontal lines x = a and x = b is

Area

In this interval.  Hence the area is given by

Apply  limits

The area of  the region bounded by  the given curves  is 1/4.