How do you find the area between f(y)=y(2y),g(y)=y?

2 Answers
Jun 3, 2018

92units2

Explanation:

Claculating the intersection Points:
x(2x)=x
so we get
x(3x)=0
So we have
x1=0
or
x2=3
and we have
30(x(2x)+x)dx=30(3xx2)dx=92

Jun 3, 2018

A=30(3yy2)dy=[32y213y3]30=92

Explanation:

The area between two curves due to y-axis is given by :

A=bax2x1dy

x2=2yy2

x1=y

lets find the cross between the curves:

2yy2=yy23y=0y(y3)=0

y=3ory=0

A=30(2yy2)(y)dy

A=30(3yy2)dy=[32y213y3]30=92

show the wanted area below (shaded):

x2=2yy2 red curve(green)

x1=y blue curve

enter image source here