Question

What is the area of bound by the curve of 2x + y = 4, y = x, y = 0?

Answer 1

2x + y = 4, y = x, y = 0

Let point A be the intersection of:

2x + y = 4, y = x

2x + x = 4

3x = 4

x = 4/3, y = 4/3

∴ A(4/3, 4/3)

Let point B be the intersection of:

2x + y = 4, y = 0

2x = 4

x = 2

∴ B(2, 0)

Let point C be the intersection of:

y = x, y = 0

x = 0, y = 0

∴ C(0, 0)

Area of the triangle with vertices A(x₁, y₁), B(x₂, y₂) and C(0, 0) is:

Area = 1/2|x₁ y₂ - x₂ y₁|

In this case area of triangle ABC is:

A = 1/2|4/3 x 0 - 2 x 4/3|

A = 1/2|0 - 8/3|

A = 1/2|-8/3|

A = 1/2 x 8/3

A = 4/3 square units.