Find the area of the region R, enclosed by:
x+2y=0 and x+y^2=3
First let's see where they intersect...
Subtracting the second equation from the first gives
and the corresponding values are and respectively.
Now, if we decide to use horizontal strips, they are bounded on the left by the line and they are bounded on the right by the curve . When we sum all these strips, they are bounded below by and bounded above by .
So the double integral is
Now why not try using vertical strips to see if you get the same answer?