Answer to Question #214043 in Calculus for sbuda

Question #214043

Determine the area enclosed by y =x and

y =x^2


1
Expert's answer
2021-07-06T10:52:04-0400

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

y=x2.....(2)y=x^2.....(2)

From equation (1) and (2)

x=x2x=x^2

or xx2=0x-x^2=0

x=0,1x=0,1

But y=xy=x

y=0,1y=0,1

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

A=01(xx2)dxA=\int_0^1(x-x^2) dx

=[x2/2x3/3]01=[{x^2/2} - {x^3/3}]_0^1

=[1/21/3][00]=[1/2-1/3]-[0-0]

=1/6=1/6 square units


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