00:01
For this problem, we are asked to use an iterated integral to find the area of the region bounded by the graphs of the equations 2x minus 3 y equals 0, x plus y equals 5, and y equals 0.
00:12
So the first thing that i'll note is that we can get out of this two different straight lines, or in fact three different straight lines.
00:18
Particularly, we would have that y equals 2x over 3, y equals 5 minus x, and lastly y equals 0.
00:27
So we would want to go through and find the points of intersection of these different equations.
00:35
Specifically, we'd have y or label them as y1, y2, y3.
00:42
We'd have y1 equals y3 when x equals 0.
00:46
We'd have y1 equals y2 when we have that 2x over 3 equals 5 minus x.
00:54
So we add x to both sides.
00:57
That would be, let's see here, 2x over 3 plus 3.
01:00
So that would be when 5x over 3 equals 5.
01:04
So, one second, something seems off here.
01:07
Oh, never mind.
01:08
So this would be when 5x equals 15, which then means that that will be when x equals 3.
01:16
And we would have that y at that point, 5 minus 3...