Answer to Question #214043 in Calculus for sbuda

Question

Determine the area enclosed by y =x and

y =x^2

Answer 1

$y=x.... (1)$

$y=x^2.....(2)$

From equation (1) and (2)

$x=x^2$

or $x-x^2=0$

$x=0,1$

But $y=x$

$y=0,1$

$(0,0)$ and $(1, 1)$ are points of intersection

$A=\int_0^1(x-x^2) dx$

$=[{x^2/2} - {x^3/3}]_0^1$

$=[1/2-1/3]-[0-0]$

$=1/6$ square units