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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.
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