Let R be the shaded region graphed below.
Use integration with vertical strips to find the area of R.
We slice R into vertical strips of width Δ x:
The strip at position x has approximate height
2 – y = 2 – 2x.
This means the area of that strip is approximately
(2 – 2x) Δ x.
Summing the areas and letting the number of strips go to ∞, we find that the area of R is