Question

the area enclosed between the curves y²=x and y=x is ? plz explain

Answer 1

y=x    and  y = x^2

First we need to find the points of intersection that bounded area:

==> y = y

==> x^2 = x

==> x^2 - x = 0

==> x(x-1) = 0

Then x = 0   and x= 1

Then we will find the area between x^2 x = 0, and x= 1

==> We know that the area is:

A1 =  intg y = intg x  dx = x^2 /2

==> A1 = (1/2 - 0) = 1/2

== A2 = intg y= intg x^2 = x^3/3

==> A2 = ( 1/3- 0 ) = 1/3

Then the area is:

 A = A1 - A2 = 1/2  - 1/3 = 1/6