Question

Sketch and find the area of theregion bounded by the given curves. Choose the variable of integration so that the area is written as a single integral. y = x, y = 2 – x, y = 0

Answer 1

To write the area as a single integral, you'll have to integrate with respect to \(y\):

Answer 2

okay

Answer 3

so i'll be integrating those 3 right?

Answer 4

First you have to write the curves as a function of y:
\[y=x~\Rightarrow~x=y\\
y=2-x~\Rightarrow~x=2-y\]