This is a document for calculating the area between two curves.

1. Question:
Find the area between the curves x+y=5 and x+2y=6.They are both straight lines.
Solution:
I have drawn a graph of the two curves. The red line represents the line x+y=5 and the blue line
represents the line x+2y=6.
The given equations are x+y=5 and x+2y=6.
The first equation is x+y=5.It can be rewritten as y=5-x.
The first function f(x)=y=5-x
The second equation is x+2y=6.It can be rewritten as y=((6-x)/2)
The second function g(x)=y=
6−𝑥
2
Subtracting the first equation from the second equation we get, y=1

2. Substituting in the first equation we get x=4.
The lines intersect at the point P(4,1).
According to Calculus, Area of the region between the two curves is A=∫ [𝑓(𝑥) − 𝑔(𝑥)]𝑑𝑥
𝑥2
𝑥1
The value of x ranges from 0 to 4.
x1=0 and x2=4 for the integral limit values.
Plugging in the values, we get A=∫ [5 − 𝑥 − (
6−𝑥
2
4
0
)]𝑑𝑥=∫ [5 − 𝑥 − 3 + (
𝑥
2
4
0
)]dx=∫ (2 − (
𝑥
2
4
0
))𝑑𝑥
=[2x-(
𝑥^2
4
)] from 0 to 4 {By using the properties of definite integrals}
Plugging in the values,
=2(4-0)-(
16−0
4
)
=8-4
=4 square units.
This region lies above the x-axis in the first quadrant in the cartesian plane.
Area between the two curves=4 square units.