Question

What is the area bounded by `y_1=x,y_2=2-x,y_3=0`?

Answer 1

You should draw these lines, and you'll see it's a triangle.

Let's look at the intersections, because they form the corners of the triangle.

`y_1=x`
`y_2=2-x`
`y_3=0` (the `x`-axis)

`y_1 andy_2` give `(1,1)` top
`y_1 and y_3` give `(0,0)` lower left corner
`y_2andY_3` give `(2,0)` lower right corner

We now have a triangle with base `b=2` and height `h=1`

Area = `1/2*b*h=1/2*2*1=1`