region bounded

Question

Find the area of the region bounded by the graphs of y = x, y = -x + 4, and y = 0.  

4

2

8

None of these

Answer 1

Via horizontal strip:

 

First you need to get the intersection of the equation to set the limit.

 

x=y

y=-x+4

 

y=-y+4; y=2, x=2

 

Since it's horizontal strip, we're gonna look at the y values for limit, that would be the x-axis (y=0) and the intersection (y=2).

 

Next we're gonna subtract the equation on the right of the graph by the one at the left in terms of y.

 

Change the equations first in terms of y: x=y and x=-y+4

 

Subtract those and integrate with limits of 0 to 2. Integral((-y+4)-y) 0 to 2 = 4

 

*It will be a little hard to understand without the graph but I hope you get it.