find the area bounded by curves xy=2 and y=4 and 4y =x*x

First we caluculate the intersection points of the given Equations.

y=2/x and y=4   intersection point is x=1/2

y=4 and y=x^2/4 inter section point is x=4

y=2/x and y=x^2/4 intersection point is x=2

We use definite integration for finding the area of the graphs.

first

A1=    integral 1/2 to 2 (2/x)=ln8

 A2=   integral 2 to 4 (x^2/4)=14/3

 A3=   integral 1/2 to 2 (4)=6

A4=    integral 2 to 4  (4)=8

A5=A3-A1=6-ln8

                =6-2.079

                =3.921

A6=A4-A2

    =8-(14/3)

    =10/3

    =3.33

Therefore the area between the given equations is A5+A6=3.921+3.33

                                                                         =7.25 square units.

To understand this problem draw the graphs of equations.

Regards to you.Happy learning.

Hari krishna.